Construction of Drug–Polymer Thermodynamic Phase Diagrams Using Flory–Huggins Interaction Theory: Identifying the Relevance of Temperature and Drug Weight Fraction to Phase Separation within Solid Dispersions

Amorphous drug-polymer solid dispersions have the potential to enhance the dissolution performance and thus bioavailability of BCS class II drug compounds. The principle drawback of this approach is the limited physical stability of amorphous drug within the dispersion. Accurate determination of the solubility and miscibility of drug in the polymer matrix is the key to the successful design and development of such systems. In this paper, we propose a novel method, based on Flory-Huggins theory, to predict and compare the solubility and miscibility of drug in polymeric systems. The systems chosen for this study are (1) hydroxypropyl methylcellulose acetate succinate HF grade (HPMCAS-HF)-felodipine (FD) and (2) Soluplus (a graft copolymer of polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol)-FD. Samples containing different drug compositions were mixed, ball milled, and then analyzed by differential scanning calorimetry (DSC). The value of the drug-polymer interaction parameter ? was calculated from the crystalline drug melting depression data and extrapolated to lower temperatures. The interaction parameter ? was also calculated at 25 °C for both systems using the van Krevelen solubility parameter method. The rank order of interaction parameters of the two systems obtained at this temperature was comparable. Diagrams of drug-polymer temperature-composition and free energy of mixing (?G mix) were constructed for both systems. The maximum crystalline drug solubility and amorphous drug miscibility may be predicted based on the phase diagrams. Hyper-DSC was used to assess the validity of constructed phase diagrams by annealing solid dispersions at specific drug loadings. Three different samples for each polymer were selected to represent different regions within the phase diagram

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

Locating binding poses in protein-ligand systems using reconnaissance metadynamics

A molecular dynamics-based protocol is proposed for finding and scoring protein-ligand binding poses. This protocol uses the recently developed reconnaissance metadynamics method, which employs a self-learning algorithm to construct a bias that pushes the system away from the kinetic traps where it would otherwise remain. The exploration of phase space with this algorithm is shown to be roughly six to eight times faster than unbiased molecular dynamics and is only limited by the time taken to diffuse about the surface of the protein. We apply this method to the well-studied trypsin-benzamidine system and show that we are able to refind all the poses obtained from a reference EADock blind docking calculation. These poses can be scored based on the length of time the system remains trapped in the pose. Alternatively, one can perform dimensionality reduction on the output trajectory and obtain a map of phase space that can be used in more expensive free-energy calculations.

Binding of Calcium and Carbonate to Polyacrylates

Polyacrylate molecules can be used to slow the growth of calcium carbonate. However, little is known about the mechanism by which the molecules impede the growth rate. A recent computational study (Bulo et al. Macromolecules 2007, 40, 3437) used metadynamics to investigate the binding of calcium to polyacrylate chains and has thrown some light on the coiling and precipitation of these polymers. We extend these simulations to examine the binding of calcium and carbonate to polyacrylate chains. We show that calcium complexed with both carbonate and polyacrylate is a very stable species. The free energies of calcium-carbonate-polyacrylate complexes, with different polymer configurations, are calculated, and differences in the free energy of the binding of carbonate are shown to be due to differences in the amount of steric hindrance about the calcium, which prevents the approach of the carbonate ion.

Measuring the Characteristic Function of the Work Distribution

We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid optomechanical-electromechanical devices, where the theoretical proposals discussed in our work could find an experimental demonstration.

PLUMED 2: New feathers for an old bird

Enhancing sampling and analyzing simulations are central issues in molecular simulation. Recently, we introduced PLUMED, an open-source plug-in that provides some of the most popular molecular dynamics (MD) codes with implementations of a variety of different enhanced sampling algorithms and collective variables (CVs). The rapid changes in this field, in particular new directions in enhanced sampling and dimensionality reduction together with new hardware, require a code that is more flexible and more efficient. We therefore present PLUMED 2 here a,complete rewrite of the code in an object-oriented programming language (C++). This new version introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs. It also has a simpler interface with the MD engines and provides a single software library containing both tools and core facilities. Ultimately, the new code better serves the ever-growing community of users and contributors in coping with the new challenges arising in the field.

Program summary

Program title: PLUMED 2

Catalogue identifier: AEEE_v2_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEE_v2_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Yes

No. of lines in distributed program, including test data, etc.: 700646

No. of bytes in distributed program, including test data, etc.: 6618136

Distribution format: tar.gz

Programming language: ANSI-C++.

Computer: Any computer capable of running an executable produced by a C++ compiler.

Operating system: Linux operating system, Unix OSs.

Has the code been vectorized or parallelized?: Yes, parallelized using MPI.

RAM: Depends on the number of atoms, the method chosen and the collective variables used.

Classification: 3, 7.7, 23. Catalogue identifier of previous version: AEEE_v1_0.

Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1961.

External routines: GNU libmatheval, Lapack, Bias, MPI. (C) 2013 Elsevier B.V. All rights reserved.

Detecting the work statistics through Ramsey-like interferometry

Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola et al., Phys. Rev. Lett. 110 (2013) 230602]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalize the protocol accordingly.

Out-of-equilibrium thermodynamics of quantum optomechanical systems

We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full charac- terization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.

Some current problems in perovskite nano-ferroelectrics and multiferroics: kinetically-limited systems of finite lateral size

We describe some unsolved problems of current interest; these involve quantum critical points in
ferroelectrics and problems which are not amenable to the usual density functional theory, nor to
classical Landau free energy approaches (they are kinetically limited), nor even to the Landau–
Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter)
because they are dominated by finite aperiodic boundary conditions.

Nonequilibrium Quantum Landauer Principle

Using the operational framework of completely positive, trace preserving operations and thermodynamic fluctuation relations, we derive a lower bound for the heat exchange in a Landauer erasure process on a quantum system. Our bound comes from a nonphenomenological derivation of the Landauer principle which holds for generic nonequilibrium dynamics. Furthermore, the bound depends on the nonunitality of dynamics, giving it a physical significance that differs from other derivations. We apply our framework to the model of a spin-1/2 system coupled to an interacting spin chain at finite temperature.

Activity and coke formation of nickel and nickel carbide in dry reforming: A deactivation scheme from density functional theory

Dry reforming is a promising reaction to utilise the greenhouse gases CO2 and CH4. Nickel-based catalysts are the most popular catalysts for the reaction, and the coke formation on the catalysts is the main obstacle to the commercialisation of dry reforming. In this study, the whole reaction network of dry reformation on both flat and stepped nickel catalysts (Ni(111) and Ni(211)) as well as nickel carbide (flat: Ni3C(001); stepped: Ni3C(111)) is investigated using density functional theory calculations. The overall reaction energy profiles in the free energy landscape are obtained, and kinetic analyses are utilised to evaluate the activity of the four surfaces. By careful examination of our results, we find the following regarding the activity: (i) flat surfaces are more active than stepped surfaces for the dry reforming and (ii) metallic nickel catalysts are more active than those of nickel carbide, and therefore, the phase transformation from nickel to nickel carbide will reduce the activity. With respect to the coke formation, the following is found: (i) the coke formation probability can be measured by the rate ratio of CH oxidation pathway to C oxidation pathway (r(CH)/r(C)) and the barrier of CO dissociation, (ii) on Ni(111), the coke is unlikely to form, and (iii) the coke formations on the stepped surfaces of both nickel and nickel carbide can readily occur. A deactivation scheme, using which experimental results can be rationalised, is proposed. 

Density functional theory study on the activation of molecular oxygen on a stepped gold surface in an aqueous environment: a new approach for simulating reactions in solution

The activation of oxygen molecules is an important issue in the gold-catalyzed partial oxidation of alcohols in aqueous solution. The complexity of the solution arising from a large number of solvent molecules makes it difficult to study the reaction in the system. In this work, O-2 activation on an Au catalyst is investigated using an effective approach to estimate the reaction barriers in the presence of solvent. Our calculations show that O-2 can be activated, undergoing OOH* in the presence of water molecules. The OOH* can readily be formed on Au(211) via four possible pathways with almost equivalent free energy barriers at the aqueous-solid interface: the direct or indirect activation of O-2 by surface hydrogen or the hydrolysis of O-2 following a Langmuir-Hinshelwood mechanism or an Eley-Rideal mechanism. Among them, the Eley-Rideal mechanism may be slightly more favorable due to the restriction of the low coverage of surface H on Au(211) in the other mechanisms. The results shed light on the importance of water molecules on the activation of oxygen in gold-catalyzed systems. Solvent is found to facilitate the oxygen activation process mainly by offering extra electrons and stabilizing the transition states. A correlation between the energy barrier and the negative charge of the reaction center is found. The activation barrier is substantially reduced by the aqueous environment, in which the first solvation shell plays the most important role in the barrier reduction. Our approach may be useful for estimating the reaction barriers in aqueous systems.

A Correlation between the Dynamic Viscosity and Crystallisation of Felodipine from its Amorphous Polymer Solid Dispersion

Purpose Previously, it has been reported that molecular mobility determines the rate of molecular approach to crystal surfaces, while entropy relates to the probability of that approaching molecule having the desirable configuration for further growth of the existing crystal; and the free energy dictates the probability of that molecule not returning to the liquid phase1. If we plot the crystal growth rate and viscosity of a supercooled liquid in a log-log format, the relationship between the two is linear, indicating the influence viscosity has upon crystal growth rate. However, such approximation has been derived from pure drug compounds and it is apparent that further understanding of crystallization from drug-polymer solid dispersion is required in order to stabilise drugs embedded within amorphous polymeric solid dispersions. Methods Mixtures of felodipine and polymer (HPMCAS-HF, PVPK15 and Soluplus®) at specified compositions were prepared using a Restch MM200 ball mill. To examine crystal growth within amorphous solid dispersions, samples were prepared by melting 5-10 mg of ball milled mixture at 150°C for 3-5 minutes on a glass slip pre-cleaned with methanol and acetone. All prepared samples were confirmed to be crystal free by visual observation using a polarised light microscope (Olympus BX50). Prepared samples were stored at 0% RH (P2O5), inside desiccators, maintained in ovens at 80°C. For the dynamic viscosity measurement, approximately 100-200mg ball milled mixture was heated on the base plate of a rotational rheometer at 150°C for 5 minutes and the top plate was lowered to a defined gap to form a good contact with the material. The sandwiched amorphous material was heated to 80°C and the viscosity was measured. Results The equation was used to probe the correlation of viscosity to crystal growth rate. In comparison to the value of xi in log-log equation reported from pure drug compound, a value of 1.63 was obtained for FD-polymer solid dispersions irrespective of the polymer involved. &#8733 Conclusion The high xi value suggests stronger viscosity dependence may exist for amorphous FD once incorporated with amorphous polymer.

Insight into CO Activation over Cu(100) under Electrochemical Conditions

The reduction of CO₂ on copper electrodes has attracted great attentions in the last decades, since it provides a sustainable approach for energy restore. During the CO₂ reduction process, the electron transfer to CO_ads is experimentally suggested to be the crucial step. In this work, we examine two possible pathways in CO activation, i.e. to generate COH_ads and CHO_ads, respectively, by performing the state-of-the-art constrained ab initio molecular dynamics simulations on the charged Cu(100) electrode under aqueous conditions, which is close to the realistic electrochemical condition. The free energy profile in the formation of COH_ads via the coupled proton and electron transfer is plotted. Furthermore, by Bader charge analyses, a linear relationship between C-O bond distance and the negative charge in CO fragment is unveiled. The formation of CHO_ads is identified to be a surface catalytic reaction, which requires the adsorption of H atom on the surface first. By comparing these two pathways, we demonstrate that kinetically the formation of COH_ads is more favored than that of CHO_ads, while CHO_ads is thermodynamically more stable. This work reveals that CO activation via COH_ads intermediate is an important pathway in electrocatalysis, which could provide some insights into CO₂ electroreduction over Cu electrodes.

Monte Carlo studies of phase transitions and adsorption : application to n-6 Lennard-Jones, C60 and zeolite systems

The solid-fluid transition properties of the n - 6 Lennard-Jones system are studied by means of extensive free energy calculations. Different values of the parameter n which regulates the steepness of the short-range repulsive interaction are investigated. Furthermore, the free energies of the n < 12 systems are calculated using the n = 12 system as a reference. The method relies on a generalization of the multiple histogram method that combines independent canonical ensemble simulations performed with different Hamiltonians and computes the free energy difference between them. The phase behavior of the fullerene C60 solid is studied by performing NPT simulations using atomistic models which treat each carbon in the molecule as a separate interaction site with additional bond charges. In particular, the transition from an orientationally frozen phase at low temperatures to one where the molecules are freely rotating at higher temperatures is studied as a function of applied pressure. The adsorption of molecular hydrogen in the zeolite NaA is investigated by means of grand-canonical Monte Carlo, in a wide range of temperatures and imposed gas pressures, and results are compared with available experimental data. A potential model is used that comprises three main interactions: van der Waals, Coulomb and induced polarization by the permanent electric field in the zeolite.