Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation.

The dissolution testing method described in the United States Pharmacopeia (USP) Chapter ⟨711⟩ is widely used for assessing the release of active pharmaceutical ingredients from solid dosage forms. However, extensive use over the years has revealed certain issues, including high experimental intervariability observed in specific formulations and the settling of particles in the dead zone of the vessel. To address these concerns and gain a comprehensive understanding of the hydrodynamic conditions within the USP 2 apparatus, computational fluid dynamic simulations have been employed in this study. The base design employed in this study is the 900 mL USP 2 vessel along with a paddle stirrer at a 50 rpm rotational speed. Additionally, alternative stirrer designs, including the hydrofoil, pitched blade, and Rushton impeller, are investigated. A comparison is also made between a flat-bottom tank and the USP round-bottom vessel of the same volume and diameter. Furthermore, this work examines the impact of various parameters, such as clearance distance (distance between the bottom of the impeller and bottom of the vessel), number of impeller blades, impeller diameter, and impeller attachment angle. The volume-average shear rate (Stv), fluid velocity (Utv), and energy dissipation rates (ϵtv) represent the key properties evaluated in this study. Comparing the USP2 design and systems with the same stirrer but flat-bottom vessel reveals more homogeneous mixing compared to the USP2 design. Analyzing fluid flow streamlines in different designs demonstrates that hydrofoil stirrers generate more suspension or upward movement of fluid compared to paddle stirrers. Therefore, when impellers are of a similar size, hydrofoil designs generate higher fluid velocities in the coning area. Furthermore, the angle of blade attachment to the hub influences the fluid velocity in the coning area in a way that the 60° angle design generates more suspension than the 45° angle design. The findings indicate that the paddle stirrer design leads to a heterogeneous shear rate and velocity distributions within the vessel compared with the other designs, suggesting suboptimal performance. These insights provide valuable guidance for the development of improved in vitro dissolution testing devices, emphasizing the importance of optimized design considerations to minimize hydrodynamic variability, enhance dissolution characterization, and reduce variability in dissolution test results. Ultimately, such advancements hold potential for improving in vitro-in vivo correlations in drug development.

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer.

The authors present a steady-state-, particle-size-, and dose-dependent dissolution-permeation model that describes particle dissolution within the concentration boundary layer (CBL) adjacent to a semipermeable surface. It is critical to understand how particle size and dose affect the behavior of dissolving particles in the presence of a CBL adjacent to a semipermeable surface both in vivo and in vitro. Control of particle size is ubiquitous in the pharmaceutical industry; however, traditional pharmaceutical assumptions of particle dissolution typically ignore particle dissolution within the length scale of the CBL. The CBL does not physically prevent particles from traveling to the semipermeable surface (mucus, epithelial barrier, synthetic membrane, etc.), and particle dissolution can occur within the CBL thickness (δC) if the particle is sufficiently small (∼dparticle ≤ δC). The total flux (the time rate transport of molecules across the membrane surface per unit area) was chosen as a surrogate parameter for measuring the additional mass generated by particles dissolving within the donor CBL. Mass transfer experiments aimed to measure the total flux of drug using an ultrathin large-area membrane diffusion cell described by Sinko et al. with a silicone-based membrane ( Mol. Pharmaceutics 2020, 17, (7) 2319-2328, DOI: 10.1021/acs.molpharmaceut.0c00040). Suspensions of ibuprofen, a model weak-acid drug, with three different particle-size distributions with average particle diameters of 6.6, 37.4, and 240 µm at multiple doses corresponding to a range of suspension concentrations with dimensionless dose numbers of 2.94, 14.7, 147, and 588 were used to test the model. Experimentally measured total flux across the semipermeable membrane/CBL region agreed with the predictions from the proposed model, and at a range of relatively low suspension concentrations, dependent on the average particle size, there was a measurable effect on the flux due to the difference in δC that formed at the membrane surface. Additionally, the dose-dependent total flux across the membrane was up to 10% higher than the flux predicted by the standard Higuchi-Hiestand dissolution model where the effects of confinement were ignored as described by Wang et al. ( Mol. Pharmaceutics 2012, 9 (5), 1052-1066, DOI: 10.1021/mp2002818).

Percolation in two-species antagonistic random sequential adsorption in two dimensions.

We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability x_{A} of choosing an A particle for an adsorption trial reaches a critical value 0.626441(1), the A species percolates and/or the blocked sites X (those with at least one A and one B nearest neighbor) percolate. Analysis of the size-distribution exponent τ, the wrapping probabilities, and the excess cluster number shows that the percolation transition is consistent with that of ordinary percolation. We obtain an exact result for the low x_{B}=1-x_{A} jamming behavior: θ_{A}=1-x_{B}+b_{2}x_{B}^{2}+O(x_{B}^{3}), Î¸_{B}=x_{B}/(z+1)+O(x_{B}^{2}) for a z-coordinated lattice, where θ_{A} and θ_{B} are, respectively, the saturation coverages of species A and B. We also show how differences between wrapping probabilities of A and X clusters, as well as differences in the number of A and X clusters, can be used to find the percolation transition point accurately.

Data-driven discovery of the governing equations for transport in heterogeneous media by symbolic regression and stochastic optimization.

With advances in instrumentation and the tremendous increase in computational power, vast amounts of data are becoming available for many complex phenomena in macroscopically heterogeneous media, particularly those that involve flow and transport processes, which are problems of fundamental interest that occur in a wide variety of physical systems. The absence of a length scale beyond which such systems can be considered as homogeneous implies that the traditional volume or ensemble averaging of the equations of continuum mechanics over the heterogeneity is no longer valid and, therefore, the issue of discovering the governing equations for flow and transport processes is an open question. We propose a data-driven approach that uses stochastic optimization and symbolic regression to discover the governing equations for flow and transport processes in heterogeneous media. The data could be experimental or obtained by microscopic simulation. As an example, we discover the governing equation for anomalous diffusion on the critical percolation cluster at the percolation threshold, which is in the form of a fractional partial differential equation, and agrees with what has been proposed previously.

Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds p_{c} for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/p_{c} and z versus -1/ln(1-p_{c}) using the data of d'Iribarne et al. [J. Phys. A 32, 2611 (1999)JPHAC50305-447010.1088/0305-4470/32/14/002] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of zp_{c}∼4η_{c}=4.51235, where η_{c} is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for bcc and fcc lattices with 2nd and 3rd NN, and bond thresholds for the sc lattice with up to the 13th NN, are obtained by Monte Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of zp_{c}∼8η_{c}=2.7351, where η_{c} is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior p_{c}=1/(z-1) is expected to hold for large z, and the finite-z correction is confirmed to satisfy zp_{c}-1∼a_{1}z^{-x}, with x=2/3 for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21, 56 (2016)1083-648910.1214/16-EJP6] and by Xu et al. [Phys. Rev. E 103, 022127 (2021)2470-004510.1103/PhysRevE.103.022127]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of zp_{c} has universal properties, depending only on the dimension of the system and whether site or bond percolation but not on the type of lattice.

Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems.

We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the q-state Potts model with anisotropic interactions.

Critical pore radius and transport properties of disordered hard- and overlapping-sphere models.

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.

Improving Dissolution Behavior and Oral Absorption of Drugs with pH-Dependent Solubility Using pH Modifiers: A Physiologically Realistic Mass Transport Analysis.

Orally dosed drugs must dissolve in the gastrointestinal (GI) tract before being absorbed through the epithelial cell membrane. In vivo drug dissolution depends on the GI tract's physiological conditions such as pH, residence time, luminal buffers, intestinal motility, and transit and drug properties under fed and fasting conditions (Paixão, P. et al. Mol. Pharm.2018 and Bermejo, et al. M. Mol. Pharm.2018). The dissolution of an ionizable drug may benefit from manipulating in vivo variables such as the environmental pH using pH-modifying agents incorporated into the dosage form. A successful example is the use of such agents for dissolution enhancement of BCS class IIb (high-permeability, low-solubility, and weak base) drugs under high gastric pH due to the disease conditions or by co-administration of acid-reducing agents (i.e., proton pump inhibitors, H2-antagonists, and antacids). This study provides a rational approach for selecting pH modifiers to improve monobasic and dibasic drug compounds' dissolution rate and extent under high-gastric pH dissolution conditions, since the oral absorption of BCS class II drugs can be limited by either the solubility or the dissolution rate depending on the initial dose number. Betaine chloride, fumaric acid, and tartaric acid are examples of promising pH modifiers that can be included in oral dosage forms to enhance the rate and extent of monobasic and dibasic drug formulations. However, selection of a suitable pH modifier is dependent on the drug properties (e.g., solubility and pKa) and its interplay with the pH modifier pKa or pKas. As an example of this complex interaction, for basic drugs with high pKa and intrinsic solubility values and large doses, a polyprotic pH modifier can be expected to outperform a monoacid pH modifier. We have developed a hierarchical mass transport model to predict drug dissolution of formulations under varying pH conditions including high gastric pH. This model considers the effect of physical and chemical properties of the drug and pH modifiers such as pKa, solubility, and particle size distribution. This model also considers the impact of physiological conditions such as stomach emptying rate, stomach acid and buffer secretion, residence time in the GI tract, and aqueous luminal volume on drug dissolution. The predictions from this model are directly applicable to in vitro multi-compartment dissolution vessels and are validated by in vitro experiments in the gastrointestinal simulator. This model's predictions can serve as a potential data source to predict plasma concentrations for formulations containing pH modifiers administered under the high-gastric pH conditions. This analysis provides an improved formulation design procedure using pH modifiers by minimizing the experimental iterations under both in vitro and in vivo conditions.

Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

By means of extensive Monte Carlo simulation, we study extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearest neighbors for the simple cubic lattice. We find precise thresholds for 23 systems using a single-cluster growth algorithm. Site percolation on lattices with compact neighborhoods of connected sites can be mapped to problems of lattice percolation of extended objects of a given shape, such as disks and spheres, and the thresholds can be related to the continuum thresholds η_{c} for objects of those shapes. This mapping implies zp_{c}∼4η_{c}=4.51235 in two dimensions and zp_{c}∼8η_{c}=2.7351 in three dimensions for large z for circular and spherical neighborhoods, respectively, where z is the coordination number. Fitting our data for compact neighborhoods to the form p_{c}=c/(z+b) we find good agreement with this prediction, c=2^{d}η_{c}, with the constant b representing a finite-z correction term. We also examined results from other studies using this fitting formula. A good fit of the large but finite-z behavior can also be made using the formula p_{c}=1-exp(-2^{d}η_{c}/z), a generalization of a formula of Koza, Kondrat, and Suszcaynski [J. Stat. Mech.: Theor. Exp. (2014) P110051742-546810.1088/1742-5468/2014/11/P11005]. We also study power-law fits which are applicable for the range of values of z considered here.

Hierarchical Mass Transfer Analysis of Drug Particle Dissolution, Highlighting the Hydrodynamics, pH, Particle Size, and Buffer Effects for the Dissolution of Ionizable and Nonionizable Drugs in a Compendial Dissolution Vessel.

Dissolution is a crucial process for the oral delivery of drug products. Before being absorbed through epithelial cell membranes to reach the systemic circulation, drugs must first dissolve in the human gastrointestinal (GI) tract. In vivo and in vitro dissolutions are complex because of their dependency upon the drug physicochemical properties, drug product, and GI physiological properties. However, an understanding of this process is critical for the development of robust drug products. To enhance our understanding of in vivo and in vitro dissolutions, a hierarchical mass transfer (HMT) model was developed that considers the drug properties, GI fluid properties, and fluid hydrodynamics. The key drug properties include intrinsic solubility, acid/base character, pKa, particle size, and particle polydispersity. The GI fluid properties include bulk pH, buffer species concentration, fluid shear rate, and fluid convection. To corroborate the model, in vitro dissolution experiments were conducted in the United States Pharmacopeia (USP) 2 dissolution apparatus. A weakly acidic (ibuprofen), a weakly basic (haloperidol), and a nonionizable (felodipine) drug were used to study the effects of the acid/base character, pKa, and intrinsic solubility on dissolution. 900 mL of 5 mM bicarbonate and phosphate buffers at pH 6.5 and 37 °C was used to study the impact of the buffer species on drug dissolution. To investigate the impacts of fluid shear rate and convection, the apparatus was operated at different impeller rotational speeds. Moreover, presieved ibuprofen particles with different average diameters were used to investigate the effect of particle size on drug dissolution. In vitro experiments demonstrate that the dissolution rates of both the ionizable compounds used in this study were slower in bicarbonate buffer than in phosphate buffer, with the same buffer concentration, because of the lower interfacial buffer capacity, a unique behavior of bicarbonate buffer. Therefore, using surrogates (i.e., 50 mM phosphate) for bicarbonate buffer for biorelevant in vitro dissolution testing may overestimate the in vivo dissolution rate for ionizable drugs. Model simulations demonstrated that, assuming a monodisperse particle size when modeling, dissolution may overestimate the dissolution rate for polydisperse particle size distributions. The hydrodynamic parameters (maximum shear rate and fluid velocity) under in vitro conditions in the USP 2 apparatus under different rotational speeds are orders of magnitude higher compared to the in vivo situation. The inconsistencies between the in vivo and in vitro drug dissolution hydrodynamic conditions may cause an overestimation of the dissolution rate under in vitro conditions. The in vitro dissolution data supported the accuracy of the HMT for drug dissolution. This is the first drug dissolution model that incorporates the effect of the bulk pH and buffer concentration on the interfacial drug particle solubility of ionizable compounds, combined with the medium hydrodynamics effect (diffusion, convection, shear, and confinement components), and drug particle size distribution.

Bond percolation on simple cubic lattices with extended neighborhoods.

We study bond percolation on the simple cubic lattice with various combinations of first, second, third, and fourth nearest neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111. However, for large z, the threshold must approach the Bethe lattice result p_{c}=1/(z-1). Fitting our data and data for additional nearest neighbors, we find p_{c}(z-1)=1+1.224z^{-1/2}.

Renormalization group theory of percolation on pseudofractal simplicial and cell complexes.

Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems ranging from the brain to high-order social networks. Simplicial complexes are formed by simplicies, such as nodes, links, triangles, and so on. Cell complexes further extend these generalized network structures as they are formed by regular polytopes, such as squares, pentagons, etc. Pseudofractal simplicial and cell complexes are a major example of generalized network structures and they can be obtained by gluing two-dimensional m-polygons (m=3 triangles, m=4 squares, m=5 pentagons, etc.) along their links according to a simple iterative rule. Here we investigate the interplay between the topology of pseudofractal simplicial and cell complexes and their dynamics by characterizing the critical properties of link percolation defined on these structures. By using the renormalization group we show that the pseudofractal simplicial and cell complexes have a continuous percolation threshold at p_{c}=0. When the pseudofractal structure is formed by polygons of the same size m, the transition is characterized by an exponential suppression of the order parameter P_{∞} that depends on the number of sides m of the polygons forming the pseudofractal cell complex, i.e., P_{∞}∝pexp(-α/p^{m-2}). Here these results are also generalized to random pseudofractal cell complexes formed by polygons of different number of sides m.

Bond percolation between k separated points on a square lattice.

We consider a percolation process in which k points separated by a distance proportional the system size L simultaneously connect together (k>1), or a single point at the center of a system connects to the boundary (k=1), through adjacent connected points of a single cluster. These processes yield new thresholds p[over ¯]_{ck} defined as the average value of p at which the desired connections first occur. These thresholds not sharp, as the distribution of values of p_{ck} for individual samples remains broad in the limit of L→∞. We study p[over ¯]_{ck} for bond percolation on the square lattice and find that p[over ¯]_{ck} are above the normal percolation threshold p_{c}=1/2 and represent specific supercritical states. The p[over ¯]_{ck} can be related to integrals over powers of the function P_{∞}(p) equal to the probability a point is connected to the infinite cluster; we find numerically from both direct simulations and from measurements of P_{∞}(p) on L×L systems that for L→∞, p[over ¯]_{c1}=0.51755(5), p[over ¯]_{c2}=0.53219(5), p[over ¯]_{c3}=0.54456(5), and p[over ¯]_{c4}=0.55527(5). The percolation thresholds p[over ¯]_{ck} remain the same, even when the k points are randomly selected within the lattice. We show that the finite-size corrections scale as L^{-1/ν_{k}} where ν_{k}=ν/(kß+1), with ß=5/36 and ν=4/3 being the ordinary percolation critical exponents, so that ν_{1}=48/41, ν_{2}=24/23, ν_{3}=16/17, ν_{4}=6/7, etc. We also study three-point correlations in the system and show how for p>p_{c}, the correlation ratio goes to 1 (no net correlation) as L→∞, while at p_{c} it reaches the known value of 1.022.

Random sequential adsorption of particles with tetrahedral symmetry.

We study random sequential adsorption (RSA) of a class of solids that can be obtained from a cube by specific cutting of its vertices, in order to find out how the transition from tetrahedral to octahedral symmetry affects the densities of the resulting jammed packings. We find that in general solids of octahedral symmetry form less dense packing; however, the lowest density was obtained for the packing built of tetrahedra. The densest packing is formed by a solid close to a tetrahedron but with vertices and edges slightly cut. Its density is θ_{max}=0.41278±0.00059 and is higher than the mean packing fraction of spheres or cuboids but is lower than that for the densest RSA packings built of ellipsoids or spherocylinders. The density autocorrelation function of the studied packings is typical for random media and vanishes very quickly with distance.

Renormalization group for link percolation on planar hyperbolic manifolds.

Network geometry is currently a topic of growing scientific interest, as it opens the possibility to explore and interpret the interplay between structure and dynamics of complex networks using geometrical arguments. However, the field is still in its infancy. In this work we investigate the role of network geometry in determining the nature of the percolation transition in planar hyperbolic manifolds. Boettcher et al. [Nat. Comm. 3, 787 (2012)2041-172310.1038/ncomms1774] have shown that a special type of two-dimensional hyperbolic manifolds, the Farey graphs, display a discontinuous transition for ordinary link percolation. Here we investigate using the renormalization group the critical properties of link percolation on a wider class of two-dimensional hyperbolic deterministic and random manifolds constituting the skeletons of two-dimensional cell complexes. These hyperbolic manifolds are built iteratively by subsequently gluing m-polygons to single edges. We show that when the size m of the polygons is drawn from a distribution q_{m} with asymptotic power-law scaling q_{m}≃Cm^{-γ} for m≫1, different universality classes can be observed depending on the value of the power-law exponent γ. Interestingly, the percolation transition is hybrid for γ∈(3,4) and becomes continuous for γ∈(2,3].

Mass Transport Analysis of Bicarbonate Buffer: Effect of the CO2-H2CO3 Hydration-Dehydration Kinetics in the Fluid Boundary Layer and the Apparent Effective p Ka Controlling Dissolution of Acids and Bases.

The main buffering system influencing ionizable drug dissolution in the human intestinal fluid is bicarbonate-based; however, it is rarely used in routine pharmaceutical practice due to the volatility of dissolved CO2. The typical pharmaceutical buffers used fail to capture the unique aspects of the hydration-dehydration kinetics of the bicarbonate-CO2 system. In particular, CO2 is involved in a reversible interconversion with carbonic acid (H2CO3), which is the actual conjugate acid of the system, as follows CO2 + H2O ⇌ H2CO3. In contrast to ionization reactions, this interconversion does not equilibrate very rapidly compared to the diffusional processes through a typical fluid diffusion boundary layer at a solid-liquid interface. In this report, a mathematical mass transport analysis was developed for ionizable drug dissolution in bicarbonate using the rules of conservation of mass and electric charge in addition to accounting for the diffusional times and reaction rate constants of the CO2-H2CO3 interconversion. This model, which includes both the hydration reaction rate and dehydration reaction rate, we called the "reversible non-equilibrium" (RNE) model. The predictions made by this RNE approach for ionizable drug dissolution rates were compared to the experimental data generated by an intrinsic dissolution method for three ionizable drugs, indomethacin, ibuprofen, and haloperidol. The results demonstrate the superiority of predictions for the RNE approach compared to the predictions of a model assuming equilibrium between CO2 and H2CO3, as well as models ignoring reactions. The analysis also shows that bicarbonate buffer can be viewed as having an effective p Ka in the boundary layer that is different from that in bulk and is hydrodynamics-dependent.

Elucidating structure-performance relationships in whole-cell cooperative enzyme catalysis.

Cooperative enzyme catalysis in nature has long inspired the application of engineered multi-enzyme assemblies for industrial biocatalysis. Despite considerable interest, efforts to harness the activity of cell-surface displayed multi-enzyme assemblies have been based on trial and error rather than rational design due to a lack of quantitative tools. In this study, we developed a quantitative approach to whole-cell biocatalyst characterization enabling a comprehensive study of how yeast-surface displayed multi-enzyme assemblies form. Here we show that the multi-enzyme assembly efficiency is limited by molecular crowding on the yeast cell surface, and that maximizing enzyme density is the most important parameter for enhancing cellulose hydrolytic performance. Interestingly, we also observed that proximity effects are only synergistic when the average inter-enzyme distance is > ~130 nm. The findings and the quantitative approach developed in this work should help to advance the field of biocatalyst engineering from trial and error to rational design.

Percolation on branching simplicial and cell complexes and its relation to interdependent percolation.

Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of link percolation in nonamenable two-dimensional branching simplicial and cell complexes, i.e., simplicial and cell complexes in which the boundary scales like the volume. We establish the relation between the equations determining the percolation probability in random branching cell complexes and the equation for interdependent percolation in multiplex networks with interlayer degree correlation equal to one. By using this relation we show that branching cell complexes can display more than two percolation phase transitions: the upper percolation transition, the lower percolation transition, and one or more intermediate phase transitions. At these additional transitions the percolation probability and the fractal exponent both feature a discontinuity. Furthermore, by using the renormalization group theory we show that the upper percolation transition can belong to various universality classes including the Berezinskii-Kosterlitz-Thouless (BKT) transition, the discontinuous percolation transition, and continuous transitions with anomalous singular behavior that generalize the BKT transition.

Formulation predictive dissolution (fPD) testing to advance oral drug product development: An introduction to the US FDA funded '21st Century BA/BE' project.

Over the past decade, formulation predictive dissolution (fPD) testing has gained increasing attention. Another mindset is pushed forward where scientists in our field are more confident to explore the in vivo behavior of an oral drug product by performing predictive in vitro dissolution studies. Similarly, there is an increasing interest in the application of modern computational fluid dynamics (CFD) frameworks and high-performance computing platforms to study the local processes underlying absorption within the gastrointestinal (GI) tract. In that way, CFD and computing platforms both can inform future PBPK-based in silico frameworks and determine the GI-motility-driven hydrodynamic impacts that should be incorporated into in vitro dissolution methods for in vivo relevance. Current compendial dissolution methods are not always reliable to predict the in vivo behavior, especially not for biopharmaceutics classification system (BCS) class 2/4 compounds suffering from a low aqueous solubility. Developing a predictive dissolution test will be more reliable, cost-effective and less time-consuming as long as the predictive power of the test is sufficiently strong. There is a need to develop a biorelevant, predictive dissolution method that can be applied by pharmaceutical drug companies to facilitate marketing access for generic and novel drug products. In 2014, Prof. Gordon L. Amidon and his team initiated a far-ranging research program designed to integrate (1) in vivo studies in humans in order to further improve the understanding of the intraluminal processing of oral dosage forms and dissolved drug along the gastrointestinal (GI) tract, (2) advancement of in vitro methodologies that incorporates higher levels of in vivo relevance and (3) computational experiments to study the local processes underlying dissolution, transport and absorption within the intestines performed with a new unique CFD based framework. Of particular importance is revealing the physiological variables determining the variability in in vivo dissolution and GI absorption from person to person in order to address (potential) in vivo BE failures. This paper provides an introduction to this multidisciplinary project, informs the reader about current achievements and outlines future directions.

Critical percolation clusters in seven dimensions and on a complete graph.

We study critical bond percolation on a seven-dimensional hypercubic lattice with periodic boundary conditions (7D) and on the complete graph (CG) of finite volume (number of vertices) V. We numerically confirm that for both cases, the critical number density n(s,V) of clusters of size s obeys a scaling form n(s,V)∼s^{-τ}n[over ̃](s/V^{d_{f}^{*}}) with identical volume fractal dimension d_{f}^{*}=2/3 and exponent τ=1+1/d_{f}^{*}=5/2. We then classify occupied bonds into bridge bonds, which includes branch and junction bonds, and nonbridge bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree. Deleting branch bonds from percolation configurations produces leaf-free configurations, whereas deleting all bridge bonds leads to bridge-free configurations composed of blobs. It is shown that the fraction of nonbridge (biconnected) bonds vanishes, ρ_{n,CG}→0, for large CGs, but converges to a finite value, ρ_{n,7D}=0.0061931(7), for the 7D hypercube. Further, we observe that while the bridge-free dimension d_{bf}^{*}=1/3 holds for both the CG and 7D cases, the volume fractal dimensions of the leaf-free clusters are different: d_{lf,7D}^{*}=0.669(9)≈2/3 and d_{lf,CG}^{*}=0.3337(17)≈1/3. On the CG and in 7D, the whole, leaf-free, and bridge-free clusters all have the shortest-path volume fractal dimension d_{min}^{*}≈1/3, characterizing their graph diameters. We also study the behavior of the number and the size distribution of leaf-free and bridge-free clusters. For the number of clusters, we numerically find the number of leaf-free and bridge-free clusters on the CG scale as ∼lnV, while for 7D they scale as ∼V. For the size distribution, we find the behavior on the CG is governed by a modified Fisher exponent τ^{'}=1, while for leaf-free clusters in 7D, it is governed by Fisher exponent τ=5/2. The size distribution of bridge-free clusters in 7D displays two-scaling behavior with exponents τ=4 and τ^{'}=1. The probability distribution P(C_{1},V)dC_{1} of the largest cluster of size C_{1} for whole percolation configurations is observed to follow a single-variable function P[over ¯](x)dx, with x≡C_{1}/V^{d_{f}^{*}} for both CG and 7D. Up to a rescaling factor for the variable x, the probability functions for CG and 7D collapse on top of each other within the entire range of x. The analytical expressions in the x→0 and x→∞ limits are further confirmed. Our work demonstrates that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts.