On the size of quadtrees generalized to d-dimensional binary pictures

AbstractSome results about the size of quadtrees and linear quadtrees, used to represent binary 2n × 2n digital pictures, are generalized to d-dimensional 2n × … × 2n pictures. Among these results are a comparison of the space-efficiency of linear vs regular trees, in terms of both the number of nodes of the tree and the number of bits needed to store each node, and an upper bound on the number of nodes as a function of n and the perimeter of the picture

Structural Disruption of an Adenosine-Binding DNA Aptamer on Graphene: Implications for Aptasensor Design

YesWe report on the predicted structural disruption of an adenosine-binding DNA aptamer adsorbed via noncovalent interactions on aqueous graphene. The use of surface-adsorbed biorecognition elements on device substrates is needed for integration in nanofluidic sensing platforms. Upon analyte binding, the conformational change in the adsorbed aptamer may perturb the surface properties, which is essential for the signal generation mechanism in the sensor. However, at present, these graphene-adsorbed aptamer structure(s) are unknown, and are challenging to experimentally elucidate. Here we use molecular dynamics simulations to investigate the structure and analyte-binding properties of this aptamer, in the presence and absence of adenosine, both free in solution and adsorbed at the aqueous graphene interface. We predict this aptamer to support a variety of stable binding modes, with direct base−graphene contact arising from regions located in the terminal bases, the centrally located binding pockets, and the distal loop region. Considerable retention of the in-solution aptamer structure in the adsorbed state indicates that strong intra-aptamer interactions compete with the graphene−aptamer interactions. However, in some adsorbed configurations the analyte adenosines detach from the binding pockets, facilitated by strong adenosine−graphene interactions

Elucidating the mechanisms of nanodiamond-promoted structural disruption of crystallised lipid

yesThe removal or structural disruption of crystallised lipid is a pivotal but energy-intensive step in a wide range of industrial and biological processes. Strategies to disrupt the structure of crystallised lipid in aqueous solution at lower temperatures are much needed, where nanoparticle-based strategies show enormous promise. Using the aqueous tristearin bilayer as a model for crystallised lipid, we demonstrate that the synergistic use of surfactant and detonation nanodiamonds can depress the onset temperature at which disruption of the crystallised lipid structure occurs. Our simulations reveal the molecular-scale mechanisms by which this disruption takes place, indicating that the nanodiamonds serve a dual purpose. First, the nanodiamonds are predicted to facilitate delivery of surfactant to the lipid/water interface, and second, nanodiamond adsorption acts to roughen the lipid/water interface, enhancing ingress of surfactant into the bilayer. We find the balance of the hydrophobic surface area of the nanodiamond and the nanodiamond surface charge density to be a key determinant of the effectiveness of using nanodiamonds to facilitate lipid disruption. For the nanodiamond size considered here, we identify a moderate surface charge density, that ensures the nanodiamonds are neither too hydrophobic nor too hydrophilic, to be optimal

Inversion of Cycle Index Sum Relations for 2- and 3-Connected Graphs

AbstractAlgebraic inversion of cycle index sum relations is employed to derive new algorithms for counting unlabeled 2-connected graphs, homeomorphically irreducible 2-connected graphs, and 3-connected graphs. The new algorithms are significantly more efficient than earlier ones, both asymptotically and for modest values of the order. Tables of computed results are included

Distinct differences in peptide adsorption on palladium and gold: introducing a polarizable model for Pd(111)

YesMaterials-binding peptides offer promising routes to the production of tailored Pd nanomaterials in aqueous media, enabling the optimization of catalytic properties. However, the atomic-scale details needed to make these advances are relatively scarce and challenging to obtain. Molecular simulations can provide key insights into the structure of peptides adsorbed at the aqueous Pd interface, provided that the force-field can appropriately capture the relevant bio-interface interactions. Here, we introduce and apply a new polarizable force field, PdP-CHARMM, for the simulation of biomolecule–Pd binding under aqueous conditions. PdP-CHARMM was parametrized with density functional theory (DFT) calculations, using a process compatible with similar polarizable force-fields created for Ag and Au surfaces, ultimately enabling a direct comparison of peptide binding modes across these metal substrates. As part of our process for developing PdP-CHARMM, we provide an extensive study of the performance of ten different dispersion-inclusive DFT functionals in recovering biomolecule–Pd(111) binding. We use the functional with best all-round performance to create PdP-CHARMM.We then employ PdP-CHARMM and metadynamics simulations to estimate the adsorption free energy for a range of amino acids at the aqueous Pd(111) interface. Our findings suggest that only His and Met favor direct contact with the Pd substrate, which we attribute to a remarkably robust interfacial solvation layering. Replica-exchange with solute tempering molecular dynamics simulations of two experimentally-identified Pd-binding peptides also indicate surface contact to be chiefly mediated by His and Met residues at aqueous Pd(111). Adsorption of these two peptides was also predicted for the Au(111) interface, revealing distinct differences in both the solvation structure and modes of peptide adsorption at the Au and Pd interfaces. We propose that this sharp contrast in peptide binding is largely due to the differences in interfacial solvent structuring.Air Force Office for Scientfi c Research (Grant #FA9550-12-1-0226

Tristearin bilayers: structure of the aqueous interface and stability in the presence of surfactants

YesWe report results of atomistic molecular dynamics simulations of an industrially-relevant, exemplar triacylglycerol (TAG), namely tristearin (TS), under aqueous conditions, at different temperatures and in the presence of an anionic surfactant, sodium dodecylbenzene sulphonate (SDBS). We predict the TS bilayers to be stable and in a gel phase at temperatures of 350 K and below. At 370 K the lipid bilayer was able to melt, but does not feature a stable liquid–crystalline phase bilayer at this elevated temperature. We also predict the structural characteristics of TS bilayers in the presence of SDBS molecules under aqueous conditions, where surfactant molecules are found to spontaneously insert into the TS bilayers. We model TS bilayers containing different amounts of SDBS, with the presence of SDBS imparting only a moderate effect on the structure of the system. Our study represents the first step in applying atomistic molecular dynamics simulations to the investigation of TAG-aqueous interfaces. Our results suggest that the CHARMM36 force-field appears suitable for the simulation of such systems, although the phase behaviour of the system may be shifted to lower temperatures than is the case for the actual system. Our findings provide a foundation for further simulation studies of the TS-aqueous interface.vesk

Probing nano-patterned peptide self-organisation at the aqueous graphene interface

YesThe peptide sequence GrBP5, IMVTESSDYSSY, is found experimentally to bind to graphene, and ex situ atomic force microscopy indicates the formation of an ordered over-layer on graphite. However, under aqueous conditions neither the molecular conformations of the adsorbed peptide chains, nor the molecular-level spatial ordering of the over-layer, has been directly resolved. Here, we use advanced molecular dynamics simulations of GrBP5, and related mutant sequences, to elucidate the adsorbed structures of both the peptide and the adsorbed peptide over-layer at the aqueous graphene interface. In agreement with a previous hypothesis, we find GrBP5 binds at the aqueous graphene interface chiefly via the tyrosine-rich C-terminal region. Our simulations of the adsorbed peptide over-layers reveal that the peptide chains form an aggregate that does not evolve further into ordered patterns. Instead, we find that the inter-chain interactions are driven by hydrogen bonding and charge–charge interactions that are not sufficiently specific to support pattern formation. Overall, we suggest that the experimentally-observed over-layer pattern may be due to the drying of the sample, and may not be prevalent at the solvated interface. However, our simulations indicate sequence modifications of GrBP5 to promote over-layer ordering under aqueous conditions

What makes a good graphene-binding peptide? Adsorption of amino acids and peptides at aqueous graphene interfaces

YesInvestigation of the non-covalent interaction of biomolecules with aqueous graphene interfaces is a rapidly expanding area. However, reliable exploitation of these interfaces in many applications requires that the links between the sequence and binding of the adsorbed peptide structures be clearly established. Molecular dynamics (MD) simulations can play a key role in elucidating the conformational ensemble of peptides adsorbed at graphene interfaces, helping to elucidate these rules in partnership with experimental characterisation. We apply our recently-developed polarisable force-field for biomolecule–graphene interfaces, GRAPPA, in partnership with advanced simulation approaches, to probe the adsorption behaviour of peptides at aqueous graphene. First we determine the free energy of adsorption of all twenty naturally occurring amino acids (AAs) via metadynamics simulations, providing a benchmark for interpreting peptide–graphene adsorption studies. From these free energies, we find that strong-binding amino acids have flat and/or compact side chain groups, and we relate this behaviour to the interfacial solvent structuring. Second, we apply replica exchange with solute tempering simulations to efficiently and widely sample the conformational ensemble of two experimentally-characterised peptide sequences, P1 and its alanine mutant P1A3, in solution and adsorbed on graphene. For P1 we find a significant minority of the conformational ensemble possesses a helical structure, both in solution and when adsorbed, while P1A3 features mostly extended, random-coil conformations. In solution this helical P1 configuration is stabilised through favourable intra-peptide interactions, while the adsorbed structure is stabilised via interaction of four strongly-binding residues, identified from our metadynamics simulations, with the aqueous graphene interface. Our findings rationalise the performance of the P1 sequence as a known graphene binder.vesk

Non-covalent adsorption of amino acid analogues on noble-metal nanoparticles: influence of edges and vertices

YesThe operation of many nanostructured biomolecular sensors and catalysts critically hinges on the manipulation of non-covalent adsorption of biomolecules on unfunctionalised noble-metal nanoparticles (NMNPs). Molecular-level structural details of the aqueous biomolecule/NMNP interface are pivotal to the successful realisation of these technologies, but such experimental data are currently scarce and challenging to obtain. Molecular simulations can generate these details, but are limited by the assumption of non-preferential adsorption to NMNP features. Here, via first principles calculations using a vdW-DF functional, and based on nanoscale sized NMNPs, we demonstrate that adsorption preferences to NP features vary with adsorbate chemistry. These results show a clear distinction between hydrocarbons, that prefer adsorption to facets over edges/vertices, over heteroatomic molecules that favour adsorption onto vertices over facets. Our data indicate the inability of widely used force-fields to correctly capture the adsorption of biomolecules onto NMNP surfaces under aqueous conditions. Our findings introduce a rational basis for the development of new force-fields that will reliably capture these phenomena

Facet-specific adsorption of tripeptides at aqueous au interfaces: open questions in reconciling experiment and simulation

YesThe adsorption of three homo-tripeptides, HHH, YYY, and SSS, at the aqueous Au interface is investigated, using molecular dynamics simulations. We find that consideration of surface facet effects, relevant to experimental conditions, opens up new questions regarding interpretations of current experimental findings. Our well-tempered metadynamics simulations predict the rank ordering of the tripeptide binding affinities at aqueous Au(111) to be YYY > HHH > SSS. This ranking differs with that obtained from existing experimental data which used surface-immobilized Au nanoparticles as the target substrate. The influence of Au facet on these experimental findings is then considered, via our binding strength predictions of the relevant amino acids at aqueous Au(111) and Au(100)(1 × 1). The Au(111) interface supports an amino acid ranking of Tyr > HisA ≃ HisH > Ser, matching that of the tripeptides on Au(111), while the ranking on Au(100) is HisA > Ser ≃ Tyr ≃ HisH, with only HisA showing non-negligible binding. The substantial reduction in Tyr amino acid affinity for Au(100) vs Au(111) offers one possible explanation for the experimentally observed weaker adsorption of YYY on the nanoparticle-immobilized substrate compared with HHH. In a separate set of simulations, we predict the structures of the adsorbed tripeptides at the two aqueous Au facets, revealing facet-dependent differences in the adsorbed conformations. Our findings suggest that Au facet effects, where relevant, may influence the adsorption structures and energetics of biomolecules, highlighting the possible influence of the structural model used to interpret experimental binding data.Air Office of Scientific Research, Grant No. FA9550-12-1-022