Drug Delivery from A Ring Implant Attached to Intraocular Lens: An In-Silico Investigation.

Multiple iterations required to design ocular implants, which will last for the desired operational period of months or even years, necessitate the use of in-silico models for ocular drug delivery. In this study, we developed an in-silico model to simulate the flow of Aqueous Humor (AH) and drug delivery from an implant to the Trabecular Meshwork (TM). The implant, attached to the side of the intraocular lens (IOL), and the TM are treated as porous media, with their effects on AH flow accounted for using the Darcy equation. This model accurately predicts the physiological values of Intraocular Pressure (IOP) for both healthy individuals and glaucoma patients, as reported in the literature. Results reveal that the effective diffusivity of the drug within the implant is the critical parameter that can alter the bioavailability time period (BTP) from a few days to months. Intuitively, BTP should increase as effective diffusivity decreases. However, we discovered that with lower levels of initial drug loading, BTP declines when effective diffusivity falls below a specific threshold. Our findings further reveal that, while AH flow has a minimal effect on the drug release profile at the implant site, it significantly impacts drug availability at the TM.

Theory and simulations of light-induced self-assembly in colloids with quantum chemistry derived empirical potentials.

Light-induced self-assembly (LISA) is a non-invasive method for tuning material properties. Photoresponsive ligands coated on the surfaces of nanoparticles are often used to achieve LISA. We report simulation studies for a photoresponsive ligand, azobenzene dithiol (ADT), which switches from a trans-to-cis configuration on exposure to ultraviolet light, allowing self-assembly in ADT-coated gold nanoparticles (NPs). This is attributed to a higher dipole moment of cis-ADT over trans-ADT which leads to a dipole-dipole attraction facilitating self-assembly. Singh and Jha [Comput. Theor. Chem., 2021, 1206, 113492] used quantum-chemistry calculations to quantify the interaction energy of a pair of ADT ligands in their cis and trans conformations. The interaction energy between ligands was fit to a potential energy function of the Lennard-Jones (LJ) form having distinct exponents for attractive and repulsive contributions. Using this generalized equation for the ligand-ligand interaction energy, we calculated the total effective interaction energy between a pair of cis as well as trans ADT-coated NPs. Specifically, we calculated the effective interaction energies between cis/trans-NPs using discrete as well as continuous approaches. Given the limitations of experiments in probing individual ligand conformations, we also studied the effect of varying the functional ligand length on the interaction energy between NPs and identified the optimal functional ligand length to capture the steric and conformational effects. Finally, using the effective interaction energy, we obtained a generalized potential energy function, which was applied in Langevin dynamics simulations to capture self-assembly in NPs.

Hydrogen-Bonded Fibrous Nanotubes Assembled from Trigonal Prismatic Building Blocks.

In reticular chemistry, molecular building blocks are designed to create crystalline open frameworks. A key principle of reticular chemistry is that the most symmetrical networks are the likely outcomes of reactions, particularly when highly symmetrical building blocks are involved. The strategy of synthesizing low-dimensional networks aims to reduce explicitly the symmetry of the molecular building blocks. Here we report the spontaneous formation of hydrogen-bonded fibrous structures from trigonal prismatic building blocks, which were designed to form three-dimensional crystalline networks on account of their highly symmetrical structures. Utilizing different microscopic and spectroscopic techniques, we identify the structures at the early stages of the assembly process in order to and understand the growth mechanism. The symmetrical molecular building blocks are incorporated preferentially in the longitudinal direction, giving rise to anisotropic hydrogen-bonded porous organic nanotubes. Entropy-driven anisotropic growth provides micrometer-scale unidirectional nanotubes with high porosity. By combining experimental evidence and theoretical modeling, we have obtained a deep understanding of the nucleation and growth processes. Our findings offer fundamental insight into the molecular design of tubular structures. The nanotubes evolve further in the transverse directions to provide extended higher-order fibrous structures [nano- and microfibers], ultimately leading to large-scale interconnected hydrogen-bonded fiber-like structures with twists and turns. Our work provides fundamental understanding and paves the way for innovative molecular designs in low-dimensional networks.

Monte Carlo simulations of spherocylinders interacting with site-dependent square-well potentials.

Monte Carlo simulations are performed to study the self-assembly of a dilute system of spherocylinders interacting with square-well potential. The interactions are defined between randomly placed sites on the axis of the spherocylinder, akin to the interacting groups on a rigid rodlike molecule. This model therefore also serves as a minimal coarse-grained representation of a system of low molecular weight or stiff polymers with contour lengths significantly lower than the persistence length, interacting predominantly with short-range interactions (e.g., hydrogen bonding). The spherocylinder concentration, square-well interaction strength and range, and fraction of interacting sites are varied to study the phase behavior of the system. We observe the formation of dispersed, bundled, and network configurations of the system that may be compared with previous atomistic simulation results of weak polyelectrolytes.

Study of the Glycerol Hydrogenolysis Reaction on Cu, Cu-Zn, and Cu-ZnO Clusters.

Quantum chemistry calculations have been performed to access the efficacy of Cu-based catalysts in various mechanistic steps of the glycerol hydrogenolysis reaction. Calculations are first performed for reactants in the gas phase (noncatalyzed system) and reactants in the gas phase with a 3-atom Cu cluster (catalyzed system). We demonstrate that the glycerol to ethylene glycol conversion is preferred in the noncatalyzed system but glycerol conversion to 1,2-propanediol via the 2-acetol intermediate is preferred in the catalyzed system. We next analyze the adsorption energies of the reactant and product species involved in the glycerol to 1,2-PDO reaction on an 8-atom Cu cluster and Cu cluster doped with a Zn atom or a ZnO molecule. Finally, we study the effects of Zn or ZnO doping on the activation barriers of the two steps of the glycerol to 1,2-PDO reaction.

Studying Drug Release through Polymeric Controlled Release Formulations in United States Pharmacopoeia 2 Apparatus Using Multiphysics Simulation and Experiments.

In vitro dissolution of oral drug formulations is often studied using the United States Pharmacopoeia (USP) apparatus. Although a well-stirred vessel or a perfect sink assumption is often employed in the modeling of in vitro dissolution in USP apparatus, such a limit is usually not realized in actual experimental conditions. The interplay of hydrodynamics in the vessel and the swelling and erosion of dosage forms often results in substantial deviations from the dissolution behavior obtained under perfect sink approximation. We develop a multiphysics model of drug release from controlled release tablets of polymeric excipients with active pharmaceutical ingredients (APIs). Simulations are performed in COMSOL for the USP 2 (paddle) apparatus and the effects of stirring speed, drug loading, erosion rate, and polymer swelling and erosion are analyzed in detail. We demonstrate that the drug release phenomena can be conveniently interpreted using the Weibull equation to fit the simulation results. This is further confirmed using drug release experiments performed on mechanically compressed tablets of naproxen sodium as the API with poly-methyl-methacrylate-co-methacrylic acid as the excipient. We show that the API-to-polymer ratio may be varied to obtain different regimes of controlled release.

Experiments and modeling of controlled release behavior of commercial and model polymer-drug formulations using dialysis membrane method.

Standard dissolution testing methods typically do not correlate strongly with the in vivo drug release behavior for the oral delivery products, since they only focus on the drug dissolution in the gastric/intestinal fluid and do not account for the intestinal absorption of drug. Artificial gastrointestinal systems attempt to bridge this gap by using dialysis membranes as a proxy for the intestinal membranes. We present a systematic proof-of-concept study of how the drug dissolution and drug absorption are mimicked in such systems for the case of polymer-drug formulations. We utilize a modified version of the conventional shaking-flask test, in which the drug formulation is placed inside a dialysis bag. Dissolution experiments are performed on a commercial aspirin formulation and model formulations of aspirin with varying amounts of poly-methyl-methacrylate-co-methacrylic acid (PMA-MAA), both for conventional and modified shaking-flask test. Results are successfully interpreted using a simple model that assumes first-order kinetics for both the drug release from the formulation and drug permeation through the membrane. The differences between the model and commercial formulations and the effects of shaking speed and drug loading are established by comparison of the first-order rate constants. Finally, comparison with a reported in vivo study demonstrates how the modified shaking-flask setup can be used to improve the in vitro in vivo correlation. Graphical abstract.

Effect of size and charge asymmetry on aggregation kinetics of oppositely charged nanoparticles.

We report a theoretical and experimental study of the aggregation kinetics of oppositely charged nanoparticles. Kinetic Monte Carlo simulations are performed for symmetric, charge-asymmetric and size-asymmetric systems of oppositely charged nanoparticles. Simulation results show that both the weight and number average aggregate size kinetics exhibit power law scaling with different exponents for small and intermediate time of evolution. The qualitative behavior of the symmetric and the size asymmetric system are the same, but the charge asymmetric system shows anomalous behavior for intermediate to high particle concentrations. We also observe a strong dependence of power law exponents on the particle concentration. Radius of gyration of the cluster that indicates how nanoparticles inside a cluster are distributed around the center of mass of the cluster shows a non-monotonic time evolution with pronounced peak at higher particle concentration. The dependence of particle concentration on aggregation kinetics as observed by predictive numerical simulation is further verified experimentally by monitoring the time evolution of aggregate size of nanoparticles assemblies of Poly (methacrylic acid) (PMMA) nanoparticles functionalized with oppositely charged ligands. These size and charge tunable asymmetric polymeric nanoparticles were synthesized by modified miniemulsion technique. The integrated approach for studying nanoparticles aggregation as described here renders new insights into super structure formation and morphology optimization which can be potentially useful in the design of new materials, such as organic photovoltaics.

Molecular Insights into the Effects of Media-Drug and Carrier-Drug Interactions on pH-Responsive Drug Carriers.

We have performed two sets of all atom molecular dynamics (MD) simulations of poly(acrylic acid) (PAA) oligomers, considered as a model pH-responsive drug carrier. In the first set, multiple oligomers of PAA are simulated in model gastric and intestinal fluids, where the degree of deprotonation of PAA oligomers is varied with the medium pH. Since the gastric fluid has a pH substantially lower than that of intestinal fluid, PAA is relatively lesser ionized in gastric fluid and forms aggregates. In the second set, we simulated multiple oligomers of PAA with multiple molecules of a cationic anticancer drug, doxorubicin (DOX), for a range of pH values representative of various physiological conditions. The diffusion coefficient of DOX decreases with an increase in pH due to an increase in the ionic complexation of PAA with DOX, despite a decrease in PAA aggregation. Our findings are in agreement with recent experimental reports on pH-triggered targeting of tumor cells by the PAA-DOX system. Results of these two sets of studies establish that both carrier aggregation and carrier-drug interactions are competing influences that together determine the drug release from pH-responsive polymers.

Mathematical Models for Controlled Drug Release Through pH-Responsive Polymeric Hydrogels.

Hydrogels consisting of weakly charged acidic/basic groups are ideal candidates for carriers in oral delivery, as they swell in response to pH changes in the gastrointestinal tract, resulting in drug entrapment at low pH conditions of the stomach and drug release at high pH conditions of the intestine. We have developed 1-dimensional mathematical models to study the drug release behavior through pH-responsive hydrogels. Models are developed for 3 different cases that vary in the level of rigor, which together can be applied to predict both in vitro (drug release from carrier) and in vivo (drug concentration in the plasma) behavior of hydrogel-drug formulations. A detailed study of the effect of hydrogel and drug characteristics and physiological conditions is performed to gain a fundamental insight into the drug release behavior, which may be useful in the design of pH-responsive drug carriers. Finally, we describe a successful application of these models to predict both in vitro and in vivo behavior of docetaxel-loaded micelle in a pH-responsive hydrogel, as reported in a recent experimental study.

Assessing the efficiency of polymeric excipients by atomistic molecular dynamics simulations.

We have performed all-atom molecular dynamics simulations of aqueous solutions of model oligomers of hydroxypropyl methylcellulose (HPMC) and hydroxypropyl methylcellulose acetate succinate (HPMCAS) excipients interacting with a representative poorly soluble active pharmaceutical ingredient (API), phenytoin. Simulations reveal formation of excipient-API complexes for some of the oligomers, which results in a reduction of API aggregation. API aggregation and diffusivity decreased with an increase in excipient content. Excipients form a "gel-like" phase spanning the simulation box beyond ∼10 wt %; API diffusivity within this gel phase is much smaller than API diffusivity without excipient, and decreases exponentially, by 5 orders of magnitude, with increased polymer concentration. Substantial differences are observed with variations in methyl, hydroxypropyl, acetate, and succinate substitution levels in the model oligomers and with the deprotonation state of succinate groups, with strongest interactions with hydrophobic phenytoin observed in the case of acetate substitution. These are used to develop quantitative measures of excipient-API interactions and excipient efficiency in the inhibition of API aggregation. We also find that for model oligomers based on Methocel E (manufactured by Dow Pharma & Food Solutions) chemistry, oligomers of length 10 monomers and simulation boxes of size 7 nm give results similar to those for longer oligomers and bigger boxes. The quantitative measures developed in this study are expected to prove useful as computational screening tools in excipient design.

Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization.

We performed kinetic Monte Carlo simulations on a model of a polymerization process in the presence of a periodic oscillatory flow to explore the role of mixing in polymerization reactors. Application of an oscillatory flow field helps overcome the diffusive limitations that develop during a polymerization process due to an increase in the molecular weights of polymer chains, thereby giving rise to high rates of polymerization. A systematic increase in the flow strength results in a "dynamic" coil-stretch transition, leading to an elongation of polymer chains. Reactive ends of stretched (polymer) chains react more frequently than the reactive ends of coiled chains, which are screened by other monomers of the same chain. There exists a critical flow strength for the efficiency of polymerization processes. The kinetic Monte Carlo simulation scheme developed here exhibit great promise for the study of dynamic properties of polymer systems.

A practical integral equation for the structure and thermodynamics of hard sphere Coulomb fluids.

A closure for the Ornstein-Zernike equation is presented, applicable for fluids of charged, hard spheres. From an exact, but intractable closure, we derive the radial distribution function of nonlinearized Debye-Hückel theory by subsequent approximations, and use the information to formulate a new closure by an extension of the mean spherical approximation. The radial distribution functions of the new closure, coined Debye-Hückel-extended mean spherical approximation, are in excellent agreement with those resulting from the hyper-netted chain approximation and molecular dynamics simulations, in the regime where the latter are applicable, except for moderately dilute systems at low temperatures where the structure agrees at most qualitatively. The method is numerically more efficient, and more important, convergent in the entire temperature-density plane. We demonstrate that the method is accurate under many conditions for the determination of the structural and thermodynamic properties of homogeneous, symmetric hard-sphere Coulomb systems, and estimate it to be a valuable basis for the formulation of density functional theories for inhomogeneous or highly asymmetric systems.

A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics.

We report a GPU implementation in HOOMD Blue of long-range electrostatic interactions based on the orientation-averaged Ewald sum scheme, introduced by Yakub and Ronchi (J. Chem. Phys. 2003, 119, 11556). The performance of the method is compared to an optimized CPU version of the traditional Ewald sum available in LAMMPS, in the molecular dynamics of electrolytes. Our GPU implementation is significantly faster than the CPU implementation of the Ewald method for small to a sizable number of particles (∼10(5)). Thermodynamic and structural properties of monovalent and divalent hydrated salts in the bulk are calculated for a wide range of ionic concentrations. An excellent agreement between the two methods was found at the level of electrostatic energy, heat capacity, radial distribution functions, and integrated charge of the electrolytes.