Interplay between Diffusion and Bond Cleavage Reaction for Determining Release in Polymer-Drug Conjugates.

In conjugated polymeric drug delivery systems, both the covalent bond degradation rate and the diffusion of the freely moving drug particles affect the release profile of the formulation. Using Monte Carlo simulations in spherical matrices, the release kinetics resulting from the competition between the reaction and diffusion processes is discussed. For different values of the relative bond cleavage rate, varied over four orders of magnitude, the evolution of (i) the number of bonded drug molecules, (ii) the fraction of the freely moved detached drug within the polymer matrix, and (iii) the resulting fractional release of the drug is presented. The characteristic release time scale is found to increase by several orders of magnitude as the cleavage reaction rate constant decreases. The two extreme rate-limiting cases where either the diffusion or the reaction dominates the release are clearly distinguishable. The crossover between the diffusion-controlled and reaction-controlled regimes is also examined and a simple analytical formula is presented that can describe the full dependence of the release time on the bond cleavage rate constant. This simple relation is provided simply by the sum of the characteristic time for purely diffusional release and the bond cleavage decay time, which equals the inverse of the reaction rate constant.

Bubble Relaxation Dynamics in Homopolymer DNA Sequences.

Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work, we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process for both adenine-thymine (AT) and guanine-cytosine (GC) homopolymers. Bubbles of different amplitudes and widths are investigated through extensive statistics and appropriate fittings of their relaxation. Characteristic relaxation times increase with bubble amplitude and width. We show that, within the model, relaxation times are two orders of magnitude longer in GC sequences than in AT sequences. Overall, our results confirm that large bubbles leave a lasting impact on the molecule's dynamics, for times between 0.5-500 ns depending on the homopolymer type and bubble shape, thus clearly affecting long-time evolutions of the molecule.

Width Dependent Elastic Properties of Graphene Nanoribbons.

The mechanical response of graphene nanoribbons under uniaxial tension, as well as its dependence on the nanoribbon width, is presented by means of numerical simulations. Both armchair and zigzag edged graphene nanoribbons are considered. We discuss results obtained through two different theoretical approaches, viz. density functional methods and molecular dynamics atomistic simulations using empirical force fields especially designed to describe interactions within graphene sheets. Apart from the stress-strain curves, we calculate several elastic parameters, such as the Young's modulus, the third-order elastic modulus, the intrinsic strength, the fracture strain, and the Poisson's ratio versus strain, presenting their variation with the width of the nanoribbon.

Efficient Mechanical Stress Transfer in Multilayer Graphene with a Ladder-like Architecture.

We report that few graphene flakes embedded into polymer matrices can be mechanically stretched to relatively large deformation (>1%) in an efficient way by adopting a particular ladder-like morphology consisting of consecutive mono-, bi-, tri-, and four-layer graphene units. In this type of flake architecture, all of the layers adhere to the surrounding polymer inducing similar deformation on the individual graphene layers, preventing interlayer sliding and optimizing the strain transfer efficiency. We have exploited Raman spectroscopy to quantify this effect from a mechanical standpoint. The finite element method and molecular dynamics simulations have been used to interpret the above experimental findings. The results suggest that a step pyramid-like architecture of a flake can be ideal for efficient loading of layered materials embedded into a polymer and that there are two prevailing mechanisms that govern axial stress transfer, namely, interfacial shear transfer and axial transmission through the ends. This concept can be easily applied to other two-dimensional materials and related van der Waals heterostructures fabricated either by mechanical exfoliation or chemical vapor deposition by appropriate patterning. This work opens new perspectives in numerous applications, including high volume fraction composites, flexible electronics, and straintronic devices.

Uniaxially Strained Graphene: Structural Characteristics and G-Mode Splitting.

The potential use of graphene in various strain engineering applications requires an accurate characterization of its properties when the material is under different mechanical loads. In this work, we present the strain dependence of the geometrical characteristics at the atomic level and the Raman active G-band evolution in a uniaxially strained graphene monolayer, using density functional theory methods as well as molecular dynamics atomistic simulations for strains that extend up to the structural failure. The bond length and bond angle variations with strain, applied either along the zigzag or along the armchair direction, are discussed and analytical relations describing this dependence are provided. The G-mode splitting with strain, as obtained by first principles' methods, is also presented. While for small strains, up to around 1%, the G-band splitting is symmetrical in the two perpendicular directions of tension considered here, this is no longer the case for larger values of strains where the splitting appears to be larger for strains along the zigzag direction. Further, a crossing is observed between the lower frequency split G-mode component and the out-of-plane optical mode at the Γ point for large uniaxial strains (>20%) along the zigzag direction.

Atomistic potential for graphene and other sp2 carbon systems.

We introduce a torsional force field for sp2 carbon to augment an in-plane atomistic potential of a previous work [G. Kalosakas et al., J. Appl. Phys., 2013, 113, 134307] so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce density-functional-theory calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp2 carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane acoustic and optical modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1000 cm-1.

Graphene flakes under controlled biaxial deformation.

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm(-1)/%, and 148.2 ± 6 cm(-1)/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E2g shifts with strains and the Grüneisen parameter was observed.

Drug release from slabs and the effects of surface roughness.

We discuss diffusion-controlled drug release from slabs or thin films. Analytical and numerical results are presented for slabs with flat surfaces, having a uniform thickness. Then, considering slabs with rough surfaces, the influence of a non-uniform slab thickness on release kinetics is numerically investigated. The numerical release profiles are obtained using Monte Carlo simulations. Release kinetics is quantified through the stretched exponential (or Weibull) function and the resulting dependence of the two parameters of this function on the thickness of the slab, for flat surfaces, and the amplitude of surface fluctuations (or the degree of thickness variability) in case of roughness. We find that a higher surface roughness leads to a faster drug release.

Phonon properties of graphene derived from molecular dynamics simulations.

A method that utilises atomic trajectories and velocities from molecular dynamics simulations has been suitably adapted and employed for the implicit calculation of the phonon dispersion curves of graphene. Classical potentials widely used in the literature were employed. Their performance was assessed for each individual phonon branch and the overall phonon dispersion, using available inelastic x-ray scattering data. The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures. The temperature dependence of the phonon dispersion curves has been examined with emphasis on the doubly degenerate Raman active Γ-E2g phonon at the zone centre, where experimental results are available. The potentials used show diverse behaviour. The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

Analytical and numerical study of diffusion-controlled drug release from composite spherical matrices.

We investigate, both analytically and numerically, diffusion-controlled drug release from composite spherical formulations consisting of an inner core and an outer shell of different drug diffusion coefficients. Theoretically derived analytical results are based on the exact solution of Fick's second law of diffusion for a composite sphere, while numerical data are obtained using Monte Carlo simulations. In both cases, and for the range of matrix parameter values considered in this work, fractional drug release profiles are described accurately by a stretched exponential function. The release kinetics obtained is quantified through a detailed investigation of the dependence of the two stretched exponential release parameters on the device characteristics, namely the geometrical radii of the inner core and outer shell and the corresponding drug diffusion coefficients. Similar behaviors are revealed by both the theoretical results and the numerical simulations, and approximate analytical expressions are presented for the dependencies.

Quantifying diffusion-controlled drug release from spherical devices using Monte Carlo simulations.

We numerically calculate drug release profiles from simple spherical devices using Monte Carlo simulations, when diffusion is the dominant release mechanism. Release curves are accurately described by the stretched exponential function, also known as the Weibull function. The dependence of the two stretched exponential parameters on the size of the spherical device and the drug diffusion coefficient is investigated and simple analytical relations are provided. Release kinetics does not depend on the initial drug concentration. The obtained results are compared with predictions derived from the analytical solution of Fick's second law of diffusion.

Targets of DNA-binding proteins in bacterial promoter regions present enhanced probabilities for spontaneous thermal openings.

We mapped promoter regions of double-stranded DNA with respect to the probabilities of appearance of relatively large bubble openings exclusively due to thermal fluctuations at physiological temperatures. We analyzed five well-studied promoter regions of procaryotic type and found a spatial correlation between the binding sites of transcription factors and the position of peaks in the probability pattern of large thermal openings. Other distinct peaks of the calculated patterns correlate with potential binding sites of DNA-binding proteins. These results suggest that a DNA molecule would more frequently expose the bases that participate in contacts with proteins, which would probably enhance the probability of the latter to reach their targets. It also stands for using this method as a means to analyze DNA sequences based on their intrinsic thermal properties.

DNA dynamically directs its own transcription initiation.

It has long been known that double-stranded DNA is subject to temporary, localized openings of its two strands. Particular regions along a DNA polymer are destabilized structurally by available thermal energy in the system. The localized sequence of DNA determines the physical properties of a stretch of DNA, and that in turn determines the opening profile of that DNA fragment. We show that the Peyrard-Bishop nonlinear dynamical model of DNA, which has been used to simulate denaturation of short DNA fragments, gives an accurate representation of the instability profile of a defined sequence of DNA, as verified using S1 nuclease cleavage assays. By comparing results for a non-promoter DNA fragment, the adenovirus major late promoter, the adeno-associated viral P5 promoter and a known P5 mutant promoter that is inactive for transcription, we show that the predicted openings correlate almost exactly with the promoter transcriptional start sites and major regulatory sites. Physicists have speculated that localized melting of DNA might play a role in gene transcription and other processes. Our data link sequence-dependent opening behavior in DNA to transcriptional activity for the first time.