Next step in the development of mesoprogestins: the preclinical profile of EC313.

Introduction: The pharmacological target for progesterone, different progestins, and Selective Progesterone Receptor Modulators (SPRMs) is the nuclear progesterone receptor (PR). EC313 is a new member of a subgroup of SPRMs, mesoprogestins, which combine especially PR- agonistic and PR-antagonistic activities in one molecule. Methods: The suitable in vivo-model for the differentiation of SPRMs from the subgroup of mesoprogestins is the estrogen-primed juvenile rabbit endometrium assay (McPhail Assay). Remarkably, in contrast to other well-known SPRMs with no agonistic effects in this test, EC313 shows clear partial PR-agonistic effects that are higher than that of the well-known mesoprogestin Asoprisnil which already demonstrated remarkable clinical effectiveness for the treatment of uterine fibroids and endometriosis. The findings from the guinea pig studies presented here can be the impetus for further preclinical development of EC313. This model shows the same features for the termination of pregnancy by antiprogestins such as Mifepristone and Ulipristal acetate (UPA) in humans. Moreover, it is possible to distinguish between progestational and anti-progestational activities in the same experiment. Results: The EC313 treatment reveals PR dominance in the genital tract and inhibits unopposed estrogenic effects. In very high doses (30.0 mg/animal/day subcutaneously (s.c.)) given twice on pregnancy days 43 and 44, no premature labor was induced (in contrast to UPA, dosed at 10.0 and 30. mg/animal/day s.c.). The anti-ovulatory activity of EC313 exceeds that of Ulipristal acetate or Mifepristone. EC313 binds to the steroid receptors in vitro with a similar affinity as the natural ligand progesterone. At the glucocorticoid receptor (GR) EC313 acts as a weak inhibitor. Minor activities at the human androgen receptor (AR) and mineralocorticoid receptor (MR) are considered negligible. No binding to the estradiol receptor was detected. In contrast to some in vitro-receptor findings, estrogenic, anti-estrogenic, androgenic, anti-androgenic, glucocorticoid, and anti-glucocorticoid actions were absent in vivo. The tissue selectivity of EC313 was demonstrated previously by reducing the growth and proliferation of uterine fibroids in animal models (lowest effective dosage 0.1 mg/kg/day s.c.).. As shown in this article, the anti-fibroid activity of EC313 was confirmed with a 10 times lower dosage (0.01 mg/kg/day s.c.). It was also shown that EC313 reduces the growth of endometriotic lesions in a human xenograft immune-deficient (NOD-SCID) mice model with a comparatively very low dosage range. In the aforementioned EC313 activity model, UPA was tested as the reference compound, the clinical effectiveness of which has already been demonstrated. Discussion: For an explanation of these findings, the possibility is discussed that the mixed agonistic/antagonistic feature of EC313 is tissue target-specific based on its super-additive synergism characteristic for active bifunctional agents. In conclusion, the specific pharmacodynamic profile of this compound opens the possibility for the development of a drug with a distinct pharmaco-endocrinological profile against uterine fibroids, endometriosis, and other PR-dependent gynecological diseases.

Interplay of orientational order and roughness in simulated thin film growth of anisotropically interacting particles.

Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic the effects of shape anisotropy in the interactions of disk- or rodlike molecules with van der Waals attractions. Increasing anisotropy leads first to a preferred orientation in the film (which is close to the corresponding equilibrium transition) while the qualitative mode of roughness evolution (known from isotropic systems) does not change. At strong anisotropies, an effective step-edge (Ehrlich-Schwoebel) barrier appears and a nonequilibrium roughening effect is found, accompanied by reordering in the film which can be interpreted as the nucleation and growth of domains of lying-down disks or rods. The information on order and roughness is combined into a diagram of dynamic growth modes.

Erratum: Lattice gas study of thin-film growth scenarios and transitions between them: Role of substrate [Phys. Rev. E 103, 023302 (2021)].

This corrects the article DOI: 10.1103/PhysRevE.103.023302.

Droplet condensation in the lattice gas with density functional theory.

A density functional for the lattice gas with next-neighbor attractions (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. The density functional is constructed via an auxiliary model with hard lattice gas particles and lattice polymers to incorporate the attractions. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density ρ[over ¯] in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential µ(ρ[over ¯]) are seen upon lowering the temperature away from the critical temperature [oscillations in µ(ρ[over ¯]) in the slab portion and spiky undulations in µ(ρ[over ¯]) in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension R_{s} in the droplet region]. This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension γ(R_{s}) gave a dominant contribution ∝1/R_{s}^{2}, although the consistency of γ(R_{s}) with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution ∝lnR_{s}/R_{s}^{2} in γ(R_{s}). The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.

Density functional for the lattice gas from fundamental measure theory.

We construct a density functional for the lattice gas or Ising model on square and cubic lattices based on lattice fundamental measure theory. To treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.

Direct Correlation Function of a Crystalline Solid.

Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds, in particular, for the ordered phases: DCFs contain information about the local structure including defects and encode the thermodynamic properties of crystalline solids; they open a route to the elastic constants beyond low temperature expansions. Via a demanding numerical approach, we have explicitly calculated for the first time the DCF of a solid: based on the fundamental measure concept, we provide results for the DCF of a hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart-both in shape as well as in its order of magnitude-because it is dominated by vacancies. We provide evidence that the traditional use of liquid DCFs in functional Taylor expansions of the free energy is conceptually wrong and show that the emergent elastic constants are in good agreement with simulation-based results.

Lattice gas study of thin-film growth scenarios and transitions between them: Role of substrate.

Thin-film growth is investigated in two types of lattice gas models where substrate and film particles are different, expressed by unequal interaction energy parameters. The first is of solid-on-solid type, whereas the second additionally incorporates desorption, diffusion in the gas phase above the film and readsorption at the film (appropriate for growth in colloidal systems). In both models, the difference between particle-substrate and particle-particle interactions plays a central role for the evolution of the film morphology at intermediate times. The models exhibit a dynamic layering transition which occurs at generally lower substrate attraction strengths than the equilibrium layering transition. A second, flattening transition is found where initial island growth transforms to layer-by-layer growth at intermediate deposition times. Combined with the known roughening behavior in such models for very large deposition times, we present four global growth scenarios, charting out the possible types of roughness evolution.

Analytical classical density functionals from an equation learning network.

We explore the feasibility of using machine learning methods to obtain an analytic form of the classical free energy functional for two model fluids, hard rods and Lennard-Jones, in one dimension. The equation learning network proposed by Martius and Lampert [e-print arXiv:1610.02995 (2016)] is suitably modified to construct free energy densities which are functions of a set of weighted densities and which are built from a small number of basis functions with flexible combination rules. This setup considerably enlarges the functional space used in the machine learning optimization as compared to the previous work [S.-C. Lin and M. Oettel, SciPost Phys. 6, 025 (2019)] where the functional is limited to a simple polynomial form. As a result, we find a good approximation for the exact hard rod functional and its direct correlation function. For the Lennard-Jones fluid, we let the network learn (i) the full excess free energy functional and (ii) the excess free energy functional related to interparticle attractions. Both functionals show a good agreement with simulated density profiles for thermodynamic parameters inside and outside the training region.

Nematic and gas-liquid transitions for sticky rods on square and cubic lattices.

Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length L with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for L≥7 and of nematic type on the cubic lattice for L≥5). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In the vicinity of the gas-liquid transition, the coexistence gap of the nematic transition quickly widens. These features are different from nematic transitions in the continuum.

Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds.

Using dynamic Monte Carlo and Brownian dynamics, we investigate a floating bond model in which particles can bind through mobile bonds. The maximum number of bonds (here fixed to 4) can be tuned by appropriately choosing the repulsive, nonadditive interactions among bonds and particles. We compute the static and dynamic structure factor (intermediate scattering function) in the vicinity of the gas-liquid critical point. The static structure exhibits a weak tetrahedral network character. The intermediate scattering function shows a temporal decay deviating from a single exponential, which can be described by a double exponential decay where the two time scales differ approximately by one order of magnitude. This time scale separation is robust over a range of wave numbers. The analysis of clusters in real space indicates the formation of noncompact clusters and shows a considerable stretch in the instantaneous size distribution when approaching the critical point. The average time evolution of the largest subcluster of given initial clusters with 10 or more particles also shows a double exponential decay. The observation of two time scales in the intermediate scattering function at low packing fractions is consistent with similar findings in globular protein solutions with trivalent metal ions that act as bonds between proteins.

Growth of films with anisotropic particles: Simulations and rate equations.

By means of computer simulations and kinetic rate equations, we study the formation of a film of rod-like particles which are deposited on a substrate. The rod-rod interactions are hard with a short-range attraction of variable strength and width, and the rod-substrate interactions favor lying rods with a variable strength. For a rod aspect ratio of 5 and deposition of up to an equivalent of one monolayer of standing rods, we demonstrate a rich variety of growth modes upon variation of the three interaction parameters. We formulate rate equations for the time evolution of densities of islands composed of standing, lying, and mixed rods. Input parameters such as diffusion constants, island capture numbers, and rod reorientation free energies are extracted from simulations, while rod reorientation attempt frequencies remain as free parameters. Numerical solutions of the rate equations in a simple truncation show rough qualitative agreement with the simulations for the early stage of film growth but an extension to later stages requires to go significantly beyond this simple truncation.

Onset of anomalous diffusion in colloids confined to quasimonolayers.

It has been recently shown that a colloidal monolayer, e.g., formed at a fluid interface or by means of a suitable confining potential, exhibits anomalous collective diffusion. This is a consequence of the hydrodynamic interactions mediated by the three-dimensional (3D) ambient fluid when the particles are confined to reside on a two-dimensional (2D) manifold. We study theoretically and with numerical simulations the crossover from normal to anomalous diffusion as the particles are, in real systems, confined by a 3D external potential and thus have the possibility to fluctuate out of the 2D manifold, thus forming a quasimonolayer.

Monolayers of hard rods on planar substrates. II. Growth.

Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion.

Phase diagrams for sticky rods in bulk and in a monolayer from a lattice free-energy functional for anisotropic particles with depletion attractions.

A density functional of fundamental measure type for a lattice model of anisotropic particles with hard-core repulsions and effective attractions is derived in the spirit of the Asakura-Oosawa model. Through polymeric lattice particles of various size and shape, effective attractions of different strength and range between the colloids can be generated. The functional is applied to the determination of phase diagrams for sticky rods of length L in two dimensions, in three dimensions, and in a monolayer system on a neutral substrate. In all cases, there is a competition between ordering and gas-liquid transitions. In two dimensions, this gives rise to a tricritical point, whereas in three dimensions, the isotropic-nematic transition crosses over smoothly to a gas-nematic liquid transition. The richest phase behavior is found for the monolayer system. For L=2, two stable critical points are found corresponding to a standard gas-liquid transition and a nematic liquid-liquid transition. For L=3, the gas-liquid transition becomes metastable.

Isotropic-nematic transition for hard rods on a three-dimensional cubic lattice.

Using grand-canonical Monte Carlo (GCMC) simulations, we investigate the isotropic-nematic phase transition for hard rods of size L×1×1 on a three-dimensional cubic lattice. We observe such a transition for L≥6. For L=6, the nematic state has a negative order parameter, reflecting the co-occurrence of two dominating orientations. For L≥7, the nematic state has a positive order parameter, corresponding to the dominance of one orientation. We investigate rod lengths up to L=25 and find evidence for a very weakly first-order isotropic-nematic transition, while we cannot completely rule out a second-order transition. It was not possible to detect a density jump at the transition, despite using large systems containing several 10^{5} particles. The probability density distributions P(Q) from the GCMC simulations near the transition are very broad, pointing to strong fluctuations. Our results complement earlier results on the demixing (pseudonematic) transition for an equivalent system in two dimensions, which is presumably of Ising type and occurs for L≥7. We compare our results to lattice fundamental measure theory (FMT) and find that FMT strongly overestimates nematic order and consequently predicts a strong first-order transition. The rod packing fraction of the nematic coexisting states, however, agree reasonably well between FMT and GCMC.

Monolayers of hard rods on planar substrates. I. Equilibrium.

The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off-lattice model featuring spherocylinders with continuous positional and orientational degrees of freedom. Both models are treated using density functional theory and Monte Carlo simulations. Upon increasing the density of rods in the monolayer, there is a continuous ordering of the rods along the monolayer normal ("standing up" transition). The continuous transition also persists in the case of an external potential which favors flat-lying rods in the monolayer. This behavior is found in both the lattice and the continuum models. For the lattice model, we find very good agreement between the results from the specific DFT used (lattice fundamental measure theory) and simulations. The properties of lattice fundamental measure theory are further illustrated by the phase diagrams of bulk hard rods in two and three dimensions.

Capillary attraction induced collapse of colloidal monolayers at fluid interfaces.

We investigate the evolution of a system of colloidal particles, trapped at a fluid interface and interacting via capillary attraction, as a function of the range of capillary interactions and temperature. We address the collapse of an initially homogeneous particle distribution and of a radially symmetric (disk-shaped) distribution of finite size, both theoretically by using a perturbative approach inspired by cosmological models and numerically by means of Brownian dynamics (BD) and dynamical density functional theory (DDFT). The results are summarized in a "dynamical phase diagram", describing a smooth crossover from a collective (gravitational-like) collapse to local (spinodal-like) clustering. In this crossover region, the evolution exhibits a peculiar shock wave behavior at the outer rim of the contracting, disk-shaped distribution.

Hydrodynamic interactions induce anomalous diffusion under partial confinement.

Under partial confinement, the motion of colloidal particles is restricted to a plane or a line but their dynamics is influenced by hydrodynamic interactions mediated by the unconfined, three-dimensional flow of the embedding fluid. We demonstrate that this dimensionality mismatch induces a characteristic divergence in the collective diffusion coefficient of the colloidal subsystem. This result, independent of the specific interparticle forces in the colloid, is solely due to the kinematical constraint on the colloidal particles, and it is different from the known divergence of transport coefficients in purely one or two-dimensional fluids.

Stable and metastable hard-sphere crystals in fundamental measure theory.

Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations, and density distributions for bcc, fcc, and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger, which is based on expanding the crystal partition function in terms of the number n of free particles while the remaining particles are frozen at their ideal lattice positions. The free energies of fcc and hcp and one branch of bcc agree well with Stillinger's approach truncated at n=2. A second branch of bcc solutions features rather spread-out density distributions around lattice sites and large equilibrium vacancy concentrations and is presumably linked to the shear instability of the bcc phase. Within fundamental measure theory and the Stillinger approach (n=2), hcp is more stable than fcc by a free energy per particle of about 0.001k(B)T. In previous simulation work, the reverse situation has been found, which can be rationalized in terms of effects due to a correlated motion of at least five particles in the Stillinger picture.

Mode expansion for the density profiles of crystal-fluid interfaces: hard spheres as a test case.

We present a technique for analyzing the full three-dimensional density profiles of planar crystal-fluid interfaces in terms of density modes. These density modes can also be related to crystallinity order parameter profiles which are used in coarse-grained, phase field type models of the statics and dynamics of crystal-fluid interfaces and are an alternative to crystallinity order parameters extracted from simulations using local crystallinity criteria. We illustrate our results for the hard sphere system using finely resolved, three-dimensional density profiles from a density functional theory of fundamental measure type.