September 9, 2017
by Danilo Roccatano
Scientists have found inspiration for their ideas by observing the nature. The symmetries and regularity in the forms and patterns in Nature have been very likely the stimulus towards the foundation of the Euclidian geometry. In the 14th century, several mathematicians start to find a relation between the geometry, mathematics and natural patterns. More recently, in the 20th century, the French-American mathematician Benoit Mandelbrot (1924–2010) has introduced the concept of fractal geometry to describe forms and phenomena in science and nature that cannot otherwise be classified. It was soon clear that fractal pattern occurs everywhere in Nature. From majestic galaxies to infinitesimal molecular worlds, fractal geometry characterizes the structural assembly of stars and molecules as a consequence of invariance of scale present in these structures
All these studies evidenced that simple but powerful mathematical properties and geometric forms are recurrently used by Nature in the shape of organisms, and other natural objects and environments. You can find the golden ratio, the Fibonacci number, spirals shaped forms, and fractals everywhere even in your home garden.
In this presentation, I made an overview of the different pattern observed in Nature from a mathematical and geometric perspective. In the first, I focused the attention on the mathematical properties of the golden ratio and Fibonacci sequence exploring its relation with the plane and spatial geometry and with the number theory. In the second part, an overview of the concept of fractals with some examples of applications are provided.
The PDF version can be downloaded here: Pattern_in_Nature_8_7_2017
April 20, 2017
by Danilo Roccatano
Peptides are versatile molecules with applications spanning from biotechnology to nanomedicine. They exhibit a good capability to unbundle carbon nanotubes (CNT) by improving their solubility in water. Furthermore, they are a powerful drug delivery system since they can easily be uptake by living cells, and their high surface to volume ratio facilitates the adsorption of molecules of different nature. Therefore, understanding the interaction mechanism between peptides and CNT is important for designing novel therapeutically agents. In this paper, the mechanisms of the adsorption of antimicrobial peptide Cecropin A – Magainin 2 (CA-MA) on a graphene nanosheet (GNS) and on an ultra-short single-walled CNT are characterized using molecular dynamics simulations. The results show that the peptide coats both GNS and CNT surface through preferential contacts with aromatic side chains. The peptide packs compactly on the carbon surfaces where the polar and functionalize Lys side chains protrude into the bulk solvent. It is shown that the adsorption is strongly correlated to a loss of the peptide helical structure. In the case of the CNT, the outer surface is significantly more accessible for adsorption. Nevertheless when the outer surface is already covered by other peptides, a spontaneous diffusion, via the amidated C-terminus, into the interior of the CNT was observed within 150 ns of simulation time. We found that this spontaneous insertion into the CNT interior can be controlled by the polarity of the entrance rim. For the positively charged CA-MA peptide studied, hydrogenated and fluorinated rims, respectively, hinder and promote the insertion.
April 19, 2017
by Danilo Roccatano
Citrate Synthase (CS) is an enzyme localized in the mitochondria of our cells where it plays an important role in the aerobic respiration cycle by transforming oxaloacetate molecules (on the right side of the picture) in citrate (on the top left side) with the assistance of the acetyl-coenzyme A (CoA) molecule. As the pac-man in the famous computer game, this Pac-Enzyme diffuse along the space between the convolute cristae of mitochondria “chomping” at its encounter oxaloacetates that activate the enzyme to bind the CoA (ghosts in the playground). For each captured CoA, a new citrate molecule is then produced (score). This complex mechanism requires large conformation changes of parts of the protein (domains) whose molecular details are not yet clarified. Using molecular dynamics simulations on the ARCHER supercomputer, I am studying in collaboration with Dr. S. Hayward of the University of UEA (Norwich, UK) this enzyme to garner novel insights on structural, dynamics and thermodynamics of its functional mechanisms.
The following image was submitted to ARCHER Image Competition 2016
and it was selected for the September picture in the ARCHER calendar 2017.
October 20, 2016
by Danilo Roccatano
In my recent public talk at the Gravity Fields Festival 2016, I have shown several models of molecular machines, I have added some of them to this blog with the details on their construction.
The models have been generated using a small script in awk language and represented using the program VMD (http://www.ks.uiuc.edu/Research/vmd/).
The Photosynthetic Apparatus of Rhodospirillum photometricum
The photosynthetic apparatus of purple photosynthetic bacteria is particularly simple and it is located in a specialized membrane system that develops in the bacterial cytoplasm. They are composed of four integral membrane protein complexes: a peripheral LH2 antennae complexes that serve to collect light and transfer the absorbed energy to the second complex, the core-complex, which is constituted of an antenna complex (LH1) associated with the photochemical reaction center (RC). The LH1 serves to funnel the light energy to the RC where a charge separation takes place catalyzing the oxidation of a water soluble carrier. The different crystallographic structures of these components are available in the Protein Data Bank. Based on the supramolecular assembly of these proteins observed using Atomic Force Topographic (Scheuring et al. 2007), it was possible to generate a molecular model of the photosynthetic apparatus of Rsp. photometricum. The model comprises one RC-LH1 core complex surrounded by several LH2 complexes. The model is a chimera of crystallographic structures from different organism. In particular, for the LH2 was used the nonameric Rps. acidophila structure [PDB id: 1KZU (McDermott et al., 1995)].
The LH1-RC complex is based on the recent crystal structure from Thermochromatium tedium [PDB id: 4V8K (Niwa et al. Nature, 2014)]. LH2 and the core complex were first centered and aligned and then translated and rotated to their relative positions using as reference the AFM topography reported by in Scheuring et al. 2007. A DPPC lipid bilayer was also generated using the tools in the VMD program and added to the model by removing the lipid molecules overlapping with the proteins.
Two views of the model are reported below. The complete fly-by animation is here.
The Yeast V-ATPase
Vacuolar-ATPase (V-ATPase) is an ancient enzyme with remarkably diverse functions in eukaryotic organisms. It is used to acidify different organelles and as a proton pump across the plasma membranes of numerous cell types. For its functions, V-ATPases use the energy produced by ATP hydrolysis. It is generally seen as the polar opposite of ATP Synthase that uses the energy from a proton gradient to produce ATP.
The structure of the model of the Yeast V-ATPase was generated by Zhao et al. using electron microscopy add homology modeling (PDB Id: 3J9U, Zhao et al. Nature, 2015). I have just generated a DPPC lipid bilayer using the tools in the VMD program and just added to the model by removing the lipid molecules overlapping with the proteins.
A view of the model is reported below. The complete fly-by animation is here.
August 20, 2016
by Danilo Roccatano
Khadga Jung Karki, Susruta Samanta, and Danilo Roccatano*
J. Phys. Chem. B, August 2016
Astaxanthin (AXT) is a reference model of xanthophyll carotenoids, which is used in medicine and food industry, and has potential applications in nanotechnology. Because of its importance, there is a great interest in understanding its molecular properties and aggregation mechanism in water and mixed solvents. In this paper, we report a novel model of AXT for molecular dynamics simulation.
The model is used to estimate different properties of the molecule in pure solutions and in water/ethanol mixtures. The calculated diffusion coefficients of AXT in pure water and ethanol are (3.22 +/- 0.01) 10-6 cm2s-1 and (2.7+/-0.4) 10-6 cm2s-1, respectively. Our simulations also show that the content of water plays a clear effect on the morphology of the AXT aggregation in water/ethanol mixture. In up to 75% (v/v) water concentration, loosely connected network of dimers and trimers, and two-dimensional array structures are observed. At higher water concentrations, AXT molecules form more compact three-dimensional structures that are preferentially solvated by the ethanol molecules. The ethanol preferential binding and the formation of a well connected hydrogen bonding network on these AXT clusters, suggest that such preferential solvation can play an important role in controlling the aggregate structure.