Lorenzo Rovigatti

Sequence-dependent thermodynamics of a coarse-grained DNA model

We introduce a sequence-dependent parametrization for a coarse-grained DNA model [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Chem. Phys. 134, 085101 (2011)] originally designed to reproduce the properties of DNA molecules with average sequences. The new parametrization introduces sequence-dependent stacking and base-pairing interaction strengths chosen to reproduce the melting temperatures of short duplexes. By developing a histogram reweighting technique, we are able to fit our parameters to the melting temperatures of thousands of sequences. To demonstrate the flexibility of the model, we study the effects of sequence on: (a) the heterogeneous stacking transition of single strands, (b) the tendency of a duplex to fray at its melting point, (c) the effects of stacking strength in the loop on the melting temperature of hairpins, (d) the force-extension properties of single strands, and (e) the structure of a kissing-loop complex. Where possible, we compare our results with experimental data and find a good agreement. A simulation code called oxDNA, implementing our model, is available as a free software.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

Gels of DNA nanostars never crystallize

Using state-of-the-art numerical techniques, we show that, upon lowering the temperature, tetravalent DNA nanostars form a thermodynamically stable, fully bonded equilibrium gel. In contrast to atomic and molecular network formers, in which the disordered liquid is always metastable with respect to some crystalline phase, we find that the DNA nanostar gel has a lower free energy than the diamond crystal structure in a wide range of concentrations. This unconventional behavior, here verified for the first time in a realistic model, arises from the large arm flexibility of the DNA nanostars, a property that can be tuned by design. Our results confirm the thermodynamic stability of the recently experimentally realized DNA hydrogels.

Self-assembly of short DNA duplexes: from a coarse-grained model to experiments through a theoretical link

Short blunt-ended DNA duplexes comprising 6 to 20 base pairs self-assemble into polydisperse semiflexible chains due to hydrophobic stacking interactions between terminal base pairs. Above a critical concentration, which depends on temperature and duplex length, such chains order into liquid crystal phases. Here, we investigate the self-assembly of such double-helical duplexes with a combined numerical and theoretical approach. We simulate the bulk system employing the coarse-grained DNA model recently proposed by Ouldridge et al. [J. Chem. Phys., 2011, 134, 08501]. Then we evaluate the input quantities for the theoretical framework directly from the DNA model. The resulting parameterfree theoretical predictions provide an accurate description of the simulation results in the isotropic phase and theoretical values for the isotropic‐nematic phase boundaries which are in line with experimental findings. In addition, the developed theoretical framework makes it possible to provide a route to estimate the stacking free energy.

Structural properties of the dipolar hard-sphere fluid at low temperatures and densities

Through extensive state-of-the-art numerical simulations, we study the behavior of the dipolar hard sphere model at low temperatures and low densities, shedding light on a region of the phase diagram where a topological phase transition has long been thought to occur. We show that the system exhibits remarkable and unusual behaviors, like a very low density percolation locus and a stabilization of rings over chain structures. This unexpected abundance of rings comes from a delicate balance between the lower ring energy and the end-to-end chain entropy, and hints at a possible mechanism for the suppression of the gas–liquid phase separation. Our results open the possibility for refined theoretical approaches which, in addition to the previously encompassed chain and branched geometries, must also include the significant contribution arising from ring formation.

Self-assembly in chains, rings, and branches: a single component system with two critical points

We study the interplay between phase separation and self-assembly in chains, rings, and branched structures in a model of particles with dissimilar patches. We extend Wertheims first order perturbation theory to include the effects of ring formation and to theoretically investigate the thermodynamics of the model. We find a peculiar shape for the vapor-liquid coexistence, featuring reentrant behavior in both phases and two critical points, despite the single-component nature of the system. The emergence of the lower critical point is caused by the self-assembly of rings taking place in the vapor, generating a phase with lower energy and lower entropy than the liquid. Monte Carlo simulations of the same model fully support these unconventional theoretical predictions.

A comparison between parallelization approaches in molecular dynamics simulations on GPUs.

We test the relative performances of two different approaches to the computation of forces for molecular dynamics simulations on graphics processing units. A “vertex‐based” approach, where a computing thread is started per particle, is compared to an “edge‐based” approach, where a thread is started per each potentially non‐zero interaction. We find that the former is more efficient for systems with many simple interactions per particle while the latter is more efficient if the system has more complicated interactions or fewer of them. By comparing computation times on more and less recent graphics processing unit technology, we predict that, if the current trend of increasing the number of processing cores—as opposed to their computing power—remains, the “edge‐based” approach will gradually become the most efficient choice in an increasing number of cases.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

Direct Simulation of the Self-Assembly of a Small DNA Origami

By using oxDNA, a coarse-grained nucleotide-level model of DNA, we are able to directly simulate the self-assembly of a small 384-base-pair origami from single-stranded scaffold and staple strands in solution. In general, we see attachment of new staple strands occurring in parallel, but with cooperativity evident for the binding of the second domain of a staple if the adjacent junction is already partially formed. For a system with exactly one copy of each staple strand, we observe a complete assembly pathway in an intermediate temperature window; at low temperatures successful assembly is prevented by misbonding while at higher temperature the free-energy barriers to assembly become too large for assembly on our simulation time scales. For high-concentration systems involving a large staple strand excess, we never see complete assembly because there are invariably instances where two copies of the same staple both bind to the scaffold, creating a kinetic trap that prevents the complete binding of either staple. This mutual staple blocking could also lead to aggregates of partially formed origamis in real systems, and helps to rationalize certain successful origami design strategies.

Accurate phase diagram of tetravalent DNA nanostars

We evaluate, by means of molecular dynamics simulations employing a realistic DNA coarse-grained model, the phase behaviour and the structural and dynamic properties of tetravalent DNA nanostars, i.e., nanoconstructs completely made of DNA. We find that, as the system is cooled down, tetramers undergo a gas–liquid phase separation in a region of concentrations which, if the difference in salt concentration is taken into account, is comparable with the recently measured experimental phase diagram [S. Biffi, R. Cerbino, F. Bomboi, E. M. Paraboschi, R. Asselta, F. Sciortino, and T. Bellini, Proc. Natl. Acad. Sci. U.S.A. 110, 15633 (2013)]. We also present a mean-field free energy for modelling the phase diagram based on the bonding contribution derived by Wertheim in his studies of associating liquids. Combined with mass-action law expressions appropriate for DNA binding and a numerically evaluated reference free energy, the resulting free energy qualitatively reproduces the numerical data. Finally, we repor...