Drug solubilization in dog intestinal fluids with and without administration of lipid-based formulations

The use of animal experiments can be minimized with computational models capable of reflecting the simulated environments. One such environment is intestinal fluid and the colloids formed in it. In this study we used molecular dynamics simulations to investigate solubilization patterns for three model drugs (carvedilol, felodi-pine and probucol) in dog intestinal fluid, a lipid-based formulation, and a mixture of both. We observed morphological transformations that lipids undergo due to the digestion process in the intestinal environment. Further, we evaluated the effect of bile salt concentration and observed the importance of interindividual variability. We applied two methods of estimating solubility enhancement based on the simulated data, of which one was in good qualitative agreement with the experimentally observed solubility enhancement. In addition to the computational simulations, we also measured solubility in i) aspirated dog intestinal fluid samples and ii) simulated canine intestinal fluid in the fasted state, and found there was no statistical difference between the two. Hence, a simplified dissolution medium suitable for in vitro studies provided physiologically relevant data for the systems explored. The computational protocol used in this study, coupled with in vitro studies using simulated intestinal fluids, can serve as a useful prescreening tool in the process of drug delivery strategies development.


Introduction
Dogs are an important animal model for drug delivery experiments due to their similarities with the physiology and metabolism of humans, as well as ease of handling and dose scaling [1][2][3][4][5][6][7][8][9].Thus, canine models are often used to evaluate the pharmacokinetics, pharmacodynamics, and safety of new drugs [1,[10][11][12].However, to reduce, refine, and replace the use of animals in research and development (the 3Rs), there is a need for alternative methods such as in vitro and in silico models [13,14].According to the 3R concept, the use of animals in research should be done in compliance with the regulations and guidelines of the relevant authorities, and only when no other alternative methods are available.Moreover, the FDA Modernization Act 2.0 allows use of cellbased assays and computer models to investigate the safety and effectiveness of a drug, as an alternative to animal testing [15].Therefore, animal studies are not mandatory in many cases, which opens possibilities for alternative methods.
A variety of computational models can contribute to drug delivery research, and with time, replace a substantial number of wet lab experiments, including those done on animals.[16,17] Apart from the ethical aspect, computational simulations save time and resources, while often providing molecular resolution insights into the interplay between drugs, delivery systems, biological fluids, and cell membranes [18,19].Moreover, in silico simulations can be a tool for optimizing dosages and delivery methods for a specific drug molecule or the composition of the gastrointestinal fluid.
One of the key problems in the field of drug deliverylow drug solubilitycan be also addressed with computational experiments simulating advanced drug delivery systems [20].The trend in newer drug candidates is towards more lipophilic compounds, with low aqueous solubility [21].Such compounds may not produce acceptable bioavailability after oral administration without help from a formulation to enhance the dissolution rate, the solubility, or both [22].Lipid-based formulation (LBF) is a promising formulation strategy often used to improve the solubility and bioavailability of poorly watersoluble drugs.By leveraging the affinity between lipids and hydrophobic drugs, and the ability of lipids and surfactants to self-aggregate, LBFs utilize such mechanisms as micellization and emulsification to absorb and encapsulate drugs, effectively increasing their solubility and stability.It is used in several commercial products, but has not yet become a very common drug delivery system, due to stability and manufacturing issues, and the complexity of interplay with biological fluids and coadministered drugs [23][24][25][26].Nevertheless, the advantages of LBFs are not limited to improving solubility.They can also enhance the absorption of drugs across the gastrointestinal tract by modifying the physiological environment [27].Likewise, they can be used to control the release rate and to protect drugs from degradation [28,29], and to target specific regions of the body [28,30].
In a previous study by our group, we evaluated-in vivo and in vitro-the solubilization of carvedilol, a poorly water-soluble drug, in a long-chain, lipid-based formulation (type IIIA-LC).The drug solubility increased in the presence of lipids and lipid digestion products in both simulated and collected dog intestinal fluids (DIF).These findings indicate that one to two grams of LBF can enhance the solubilization of drugs in the canine intestinal tract through the effects of lipid digestion products and bile secretion.In addition, the study characterized dog intestinal fluid samples for free fatty acids and bile salts at different time points after LBF administration [31].
One of the advantages of computational simulation methods, such as molecular dynamics (MD), is the possibility it offers to control the experimental environment.This is in contrast to the number of complex processes happening in parallel in vivo or even during in vitro experiments.For example, a colloid of undigested LBF in the presence or absence of intestinal fluid can be simulated with MD and compared to a fully digested analogue.In an in vivo experiment, it would be difficult to ensure digestion had already started (which would affect the colloid composition), not to mention issues with experimentally capturing processes taking place on a scale of nanoseconds.However, all-atom MD of lipid droplets requires an extraordinary amount of computational resources and is therefore only suitable for timescales of tens to hundreds of nanoseconds.To speed up simulations and to increase the number of molecules possible to study, several coarse-grained MD force fields have been developed [32].For biological systems, the currently most popular one is Martini [33].It groups three to four heavy atoms to single representations, enabling larger systems to be simulated.It is also faster due to the smoother energy landscape that comes with the coarsely represented molecules.The Martini force field has been used for simulations of proteins [34], phospholipid membranes [35,36], nanoparticles [37], LBFs [38], and for describing the colloidal structures found in the bile and small intestinal fluid [39].
In the current study, we used DIF samples remaining from our aforementioned study to analyze the solubility of three poorly soluble drugs with a broad range of logP values: carvedilol (logP = 3), felodipine (logP = 4) and probucol (logP = 10.5).Felodipine and probucol are neutral molecules, whereas carvedilol is weakly basic.We complemented the experimental work with coarse-grained MD simulations to mimic the various concentrations of bile and phospholipids seen in the DIF samples at different time points.The paper is organized as follows.After describing the methods, we report the results of the shake flask experiments in which we measured solubility in pure dog intestinal fluids, in pure LBF (type IIIA-LC) and in a mixture of the two.Next, we compare the solubility of the three drugs in commercial dog fasted state simulated intestinal fluid (FaSSIF) and in real dog intestinal fluid samples.Thereafter we describe the self-assembly of LBF and DIF colloids in MD simulations, and highlight differences between undigested and digested states and the placement of the drug molecules in the colloidal structures.The effect of bile and phospholipid concentrations on the morphology of colloidal structure is described.Finally, we draw conclusions for the application of MD simulations of DIF and LBF, and synergistic effects with the use of dog FaSSIF.A combination of computational simulations and simulated intestinal fluids can be a powerful tool to significantly reduce animal experimentation.

Materials
Carvedilol and analytical solvents were purchased from VWR International (Sweden).Felodipine and probucol were obtained from Lundbeck (Denmark).Kolliphor EL and soybean oil were obtained from Merck (USA) and maisine 35-1 from Gattefossé (France).The LBF was made by weighing components into a glass vial, to a composition of 35% (w/w) kolliphor EL, 32.5% soybean oil and 32.5% maisine 35-1, and thereafter equilibrated on a shaking board (250 rpm) in a 37 • C incubator for 24 h.

Dog intestinal fluid samples
Dog intestinal fluid samples were obtained from a previous study [31], in which three male labrador dogs (age 3-6 years), on two different days, were administered 75 mL of water or 2 g LBF dispersed in the same volume of water.In brief, DIF were collected over 1 h, by duodenal stomas surgically applied to the dogs.Prior to administration plastic tubing was attached to the stomas.The samples used in this article were collected up to 5 min after administration of the water or LBF without drug.A wider time interval was used instead of specific time points, because the collection of DIF by stomas occurs spontaneously.Orlistat was added to the sampling tubes prior to the collection of DIF to inhibit further digestion.After collection, the samples were stored at − 80 • C until analysed.Please refer to the original study for more details [31].

Drug solubility in dog intestinal fluids and dispersed LBF
The solubilities of three active pharmaceutical ingredients (APIs)carvedilol, felodipine and probucol-were each measured separately in three different media: DIF aspirated 0-5 min after administration of water, DIF after aspirated 0-5 min after administration of dispersed LBF, and lastly, LBF dispersed in a sodium phosphate buffer (10 mM, pH 6.5).
Each experiment was performed in triplicates.A volume of 300 μL was transferred to Eppendorf tubes with enough of the carvedilol, felodipine or probucol powders to make a saturated solution with an excess of undissolved drug (4-5 mg).After brief vortexing, samples were placed in an incubator at 37 • C on a shaking board.After 24 h, samples were centrifuged for 10 min at 2300 xg at 37 • C. Thereafter, 100 μL of supernatant was removed and diluted with 900 μL cold acetonitrile before centrifugation for 10 min at 2300 xg at 4 • C. The supernatant was recovered and diluted 1-100 times with mobile phase before injection to HPLC.Sample pH was measured before and after incubation with active pharmaceutical ingredients.Statistical analysis on results was performed with Brown-Forsythe and Welch ANOVA test with Dunnett's multiple comparison.

Drug solubility in dog FaSSIF and dispersed LBF
The solubilities of the three drugs were also measured in dog FaSSIF (pH 6.5), with and without dispersed LBF, as described above.

Simulation parameters
Gromacs version 2018 was used to run the MD simulations [40][41][42].All initial conformations were made with Packmol [43].After randomly placing all compounds into the initial box, steepest descent energy A. Parrow et al. minimization was performed for 4500 steps.Equilibration steps with increasing time steps were performed up to the step of 30 fs.At the production stage, a v-rescale thermostat and a Berendsen barostat were used for temperature and isotropic pressure coupling, respectively [44,45].The time constant for pressure coupling was set to be 12 ps, whereas the corresponding time constant for temperature coupling was 4 ps.Temperature and pressure were equilibrated at 310 K and 1 atm, respectively.Reaction field electrostatics with a Coulomb cut-off of 1.1 nm were used and Van der Waals interactions were calculated with the same cut-off.Periodic boundary conditions were applied in all three dimensions.The timestep was set to 30 fs for production simulations and 10 μs simulations were run to equilibrate the initial colloids.The Martini force field (version 2.2) was used for all MD simulations [33].Selfinteractions of probucol molecules were reduced slightly to match experimental data [46].Most of the molecules used in this work (see Fig. 1) were parametrized and validated earlier and had been used in other studies [36,38,[46][47][48]; the rest were prepared according to the standard Martini 2 tutorial.

Simulated systems
We performed six series of simulations to investigate the impact of several factors on the solubilization of poorly water-soluble drugs in the presence of lipid-based formulations and dog intestinal fluid (Table 1).
In the first series, colloidal self-assembly in three types of systems was observed from initially random placement of the molecules.These three types were: LBF dispersed in water, undigested LBF in DIF (the previous plus added bile salts and phospholipids), and digested LBF in DIF.In the model of digested LBF, all triglycerides and diglycerides were replaced with monoglycerides and free fatty acids (one free fatty acid and one monoglyceride replaced a diglyceride and two free fatty acids and glyceride replaced a triglyceride; see Fig. 2a).Digested and undigested states were compared with each other to study how structural composition affected the solubilization patterns of the three model APIs.Hereafter we refer to these three systems as the defaults, for the simplicity of comparison.
In the second series of simulations, ten molecules of each API (carvedilol, felodipine, probucol) were added to the default systems to determine their preferred placement and to estimate solubilization capacity.These results were then compared with experimental solubility data.In these simulations we used 3 microseconds because we used the final configurations from the first series of simulations, and because the colloids were not restructured upon adding the 10 drug molecules.
In the third series of simulations, we varied the number of bile salt (BS) and phospholipid (PL) molecules added to the three default systems to cover the range of experimentally observed BS-PL concentration values in our previous study (see table S1) [31].These also represented the range of prandial states (from fasted to fed), which is of interest even beyond the study on dog intestinal fluids.We focused primarily on the qualitative structural differences in the colloids that formed and thus no triplicates were needed.At the same time, running simulations for longer than 3 microseconds was crucial, because the LBF molecules initially self-assembled into micellular structures in the digested state and only formed vesicles for all BS-PL concentrations after 3 to 5 microseconds.The default concentrations for BS and PL in the rest of the simulations were the average values for the early time point from the original study (i.e., 7.37 mM for the total amount of bile salts).Phospholipids were not quantified experimentally and were added as onequarter of the bile amount according to the FaSSIF version 1 (see Tables 1, 2, 3) [49,50].In all series of simulations, BS was represented as a mixture of taurocholate and taurodeoxycholate at a 1:1 ratio [50].
We also varied the concentration of APIs in a separate series of simulations.We hypothesized that as the concentration increased, the drug molecules would start aggregating either within the colloid or in the bulk.This would presumably happen upon reaching the solubilization capacity.Thus, a concentration at which aggregation occurred would be directly comparable to the experimental data.
Finally, two series with pure DIF (in the absence of LBF) were performed to estimate the effect of API solubilization patterns in intestinal fluid and the effect of interindividual variability.The first of the two included only DIF itself (Fig. 2a).In the second, the APIs were added to the final configurations taken from the first series.As concentrations were low, these simulation boxes were significantly smaller than in the systems with LBF (see Fig. 2b).Since BS and PL concentration in the sample from dog 3 were very low compared to dogs 1 and 2, we had to use a significantly bigger system to have a reasonable number of bile and phospholipids present in the box (Table 2).
A cubic simulation box with a side length of approximately 17 nm was used for the pure DIF systems.The LBF in water and LBF in DIF systems were simulated in cubic boxes with a box side of 31 to 33 nm.The box size was chosen to introduce the intestinal fluid components at a realistic concentration.In contrast, the size of the LBF colloids was close to the lower end of the range experimentally observed with dynamic light scattering (Fig. S1).The size of the undigested droplets spanned from 13 nm to 4 μm, whereas digested LBF type IIIA formed droplets of greater size, starting from approximately 130 nm in diameter.However, we simulated the colloids in both undigested and digested states using the same total weight, corresponding to a droplet with a diameter of 13 to 14 nm, for a valid direct comparison.Moreover, simulations with a 130-nm colloid would be extremely resource-demanding, making it impractical to simulate the box for 10 μs.For the same reason, one colloid was present per simulation box.Thus, the interplay between colloids did not take place in the simulations performed.
The compositions of the pure DIF and other simulation boxes are specified in Tables 2 and 3, except for the third series of simulations in which the concentrations of BS and PL were varied.

Analysis
We analysed the data using Gromacs built-in tools, VMD software, and in-house scripts [40,51].The tool "gmx rdf" was used to analyze radial distribution function (RDF), which is the likelihood of the molecules being at certain distances from a reference.The center of mass of the molecules permanently presented in the colloid was used as the reference for the RDF calculations.For the analysis of solvent accessible surface area (SASA) we used the VMD command "measure sasa".The dots were used in the figures to represent the positions of the probe while in contact with molecules' beads.We evaluated the distances between APIs and micelle molecules, as well as the number of contacts between molecules with the "gmx mindist" tool.The radius of gyration was calculated via the "gmx gyrate" command.Eccentricity was calculated as e = 1 − I min/ I aver where I min and I aver are minimum and average moments of inertia of the colloid, measured over the last five microseconds of the simulations.
In this study, we used two approaches to computationally evaluate the solubilization of the drugs in DIF and LBF.The first approach considered drug aggregation to indicate having reached the solubilization capacity limit.For this purpose, a series of simulations varying the number of API molecules was run for each drug.If a stable cluster of  even two API molecules formed in the system, it was considered an aggregation event.The critical concentration at which the loading capacity was met was defined as the point where the number of API-API contacts exceeded one.This point was identified by interpolating between simulations with increasing number of drug molecules.For probucol, we used between 5 and 100 molecules, 10 to 300 for felodipine, and 2 to 200 for carvedilol (Table S2).These different ranges in the number of drug molecules were determined from the differences in aggregation tendency for the drugs, something we assume to be intimately related to the solubility.Our simulations revealed that felodipine molecules exhibited a greater propensity to cluster at higher concentrations in the presence of DIF or LBF, in contrast to probucol and carvedilol.The former two exhibited a tendency to aggregate at lower concentrations, within the colloidal and at the interface with the aqueous phase, respectively.The second approach was based on the ratio between the contacts of APIs with micelle and with water [46].The ratio reflected the miscibility of the drug molecules with DIF and LBF.Higher values indicated higher miscibility, better colloid incorporation, and a higher solubilization ratio.

Experimental section 3.1.1. Experimentally measured solubility
The equilibrium solubility after a 24 h shake flask experiment is presented in Fig. 3.In the different media, the solubility rank order of the APIs was still the same as for the aqueous solubility, that is, highest for carvedilol followed by felodipine and probucol.All APIs had their highest solubility in the sample with aspirated DIF from dogs post-LBF consumption.Apart from that, the solubility of all APIs was comparable in pure DIF and LBF dispersed in buffer.For felodipine, differences in the solubility in the different media were not as clearcut as for the other two drugs, whereas solubility enhancement for carvedilol in post-LBF DIF was significantly higher.At the same time, the standard deviation was also the highest for carvedilol in LBF + DIF.

Applicability of dog FaSSIF
Comparison of the drug solubility in DIF samples and in dog FaSSIF showed overall good agreement (Fig. 4).The differences between the solubility values in the DIF samples and the simulated fluid were very low for felodipine and probucol, and slightly larger, yet not statistically significant, for carvedilol.The differences between solubility in LBF in DIF and LBF in FaSSIF were also statistically insignificant for all drugs.For felodipine, none of the five solubility values differed significantly from others, whereas for probucol, only the solubility values in DIF and DIF + LBF were found to be different at p < 0.005.
In all cases, the standard deviation of solubility measurements in FaSSIF or FaSSIF+LBF was lower than that in DIF or DIF + LBF, whereas the average values were approximately equal between the simulated and aspirated fluids.

Structure of simulated LBF colloids
LBF in water formed a nearly spherical micelle, with an eccentricity value of 0.23; an ideal sphere has a value of 0 (see Fig. 5a and Table 4).The lipids resided in the core and were covered with cremophor molecules.Triglycerides and diglycerides were located mostly in the center of the colloid, whereas monoglycerides were found closer to the outer micelle layers.
Upon the addition of bile salts and phospholipids present in dog intestinal fluids, the structure of the colloid changed dramatically.The shape changed (eccentricity of 0.59 and 0.52 for undigested and digested LBF systems, Table 4), as the symmetry of the micellular structure reduced significantly.The cremophor molecules, previously covering the micelle core all across the surface, aggregated in one region of the surface of the LBF colloid.The rest of the outer micelle shell was occupied by intestinal fluid components (Fig. 5b).As a result, a clear distinction could be observed within the colloid: most of the colloid was covered with bile and phospholipids, whereas part of the surface was occupied solely by cremophor mass.
The replacement of triglycerides and diglycerides with monoglycerides and free fatty acids, mimicking digestion of the LBF components, rearranged the colloid from a micelle to a vesicle (Fig. 5c).Distribution of surfactant and bile salts remained polar, and an aqueous core appeared in the center of the colloid.Meanwhile the gyration radius increased only slightly compared to the undigested LBF micelle.Phospholipids could also occasionally cover the surfactant aggregate to a small extent.
Radial distribution functions described quantitatively the trends observed visually.A clear difference could be seen between undigested and digested states, where in the former the entire core of the colloid was occupied with glycerides (first and second columns in Fig. 6).In contrast, the central part of the colloid in the digested state was partially filled with cremophor, but to a much lesser extent, compared to TG and DG in the undigested state.Upon the addition of BS and PL, cremophor clearly redistributed from a thin layer at the outskirts of the colloid to a much broader region in the undigested LBF in DIF (magenta line in columns 1 and 2 in Fig. 6).The monoglyceride distribution became broader upon adding DIF components and was comparable with the phospholipid distribution (Fig. 6 b, e, h).The bile had a comparable distribution, but with a peak slightly further from the core and closer to the water.However, in the digested state, the bile had a seemingly bimodal distribution, where at 4-5 nm from the center, the distribution was significantly lower than at 5-6 nm.Interestingly, felodipine molecules in digested LBF system showed a similar, but reversed, distribution.The combination of visual inspection and radial distribution function analysis indicates that felodipine resided at inner and outer water-vesicle interfaces, but was more likely to sit on the inner side.In contrast, the outer surface was more likely covered with bile salts.The distribution of probucol in the digested state was not bimodal, but fairly narrow with the peak at 5 nm from the colloid center.This agrees well  with the high hydrophobicity of the molecules, which causes them to occupy the middle region of the vesicle wall.Carvedilol molecules tended to aggregate at the surface of the colloid, but they were more expelled from the colloid covered with BS and PL (yellow line in Fig. 6 a,  b, c).

Affinities and contacts between the molecules
It is also important to understand how molecules in the systems interact with each other, as a way to provide insights for further development of formulation strategies.We analysed how frequently the different API molecules were in contact with molecules of all other types to evaluate their affinity to them.The data in Fig. 7 are presented as portions of the total API contacts with other molecules.Carvedilol had the most contacts with water in all simulations.However, the addition of bile and phospholipids reduced the number of aqueous contacts substantially.In both the digested and undigested states of LBF in DIF, the total portion of API contacts with water, BS, and PL, was more than three-quarters of the total contacts.At the same time, carvedilol had relatively low number of contacts with cremophor in BS-and PL-free system and practically no contact in the systems with added intestinal fluid components.Felodipine resided at the interface between water and lipids or entirely inside the colloid.As opposed to the other two drugs, felodipine had more contacts with cremophor in LBF in water.Upon the addition of DIF, the contact area was reduced between cremophor and the glycerides, resulting in fewer contacts between felodipine and the surfactant (magenta in Fig. 7 for felodipine).It increased again when the colloid underwent morphological changes from micelle to vesicle; this transformation significantly increased the number of contacts with both water and cremophor at the inner leaflet.Probucol had very few contacts with water in all three systems, but in the vesicle the number of contacts was slightly higher, as the probucol had to be screened from water by lipids from both sides.In undigested LBF in DIF, the number of contacts with cremophor was also relatively low, due to the reduction of the contact area between lipids and surfactant.
To estimate the average affinity of the drug molecules towards the rest of the molecules in the colloids, we analysed the distribution of contacts normalized by the size of the molecules, using the number of beads in a coarse-grained MD model.These data are presented in Fig. S2.Felodipine and probucol interacted the most with the triglycerides.However, normalized also to the number of molecules in the micelle, the distribution of contacts for felodipine and probucol was quite even for the undigested molecules (Fig. S3).This suggests that the higher number of contacts for specific glycerides is a result of availability, rather than intrinsic affinity.

Effect of BS-PL concentration variability
As seen in our earlier study [31], the variability of the bile concentration in dog intestinal fluids was very high, ranging between 4 mM and 22 mM (see in Table S1).It was therefore of interest to see whether the colloidal structures underwent significant changes as the bile concentration changed from the lower to the higher end of the range.We kept the LBF part of the system the same and only varied the concentration of BS and PL (the latter is always one-fourth that of the BS).One of the key tools in this part of the analysis was calculation of solvent accessible surface area.Column (a) in Fig. 8 demonstrates the entire colloids with lipids in their undigested state, whereas SASA is presented in columns (b) and (c).In the column (d) the lipids are shown as semi-transparent molecules, and the contact points with water as blue dots.First of all, at a BS concentration of 16 mM, a micelle splits in two, and at 22 mM there are already four colloids in the simulation box.It was also observed that free BS monomers were floating in the bulk already at 4 mM.However only at 16 mM was the concentration so high that the split of the initial colloid became energetically favorable.Thus, more BS molecules would then be found at the interface between water and lipids.The second observation is that the number of green dots representing the contact area between cremophor and lipids decreases as the BS concentration increases from 4 mM to 10 mM (Fig. 8b,c).It is also apparent (Fig. 8a) that magenta-colored cremophor molecules are expelled more to one pole of the colloid, whereas the rest of the surface is covered with BS and PL.As soon as the split of the colloid takes place, the trend of SASA CRE-GLY becomes more complex.

Table 4
Characterization of the colloidal shapes with gyration radius R g and eccentricity e.Both of these were calculated only for glycerides, free fatty acids and cremophor molecules.Few bile and phospholipids were present in a free form and would have heavily affected the standard deviation if they had been included.R g defines the colloid size and e the degree of sphericity.Values of eccentricity range from 0 (ideal sphere) to 1 (completely non-spherical shapes).The eccentricity of the LBF in water was relatively low, and it was significantly higher for LBF in dog intestinal fluids.In the digested form the shape is slightly more spherical.This is because cremophor is partially incorporated into the inner shells of the micelle leaving the free fatty acids and dog intestinal fluid components the most exposed to water from the colloid.

LBF in water
Undigested LBF in DIF Digested LBF in DIF R g , nm 5,33 ± 0,00 5,36 ± 0,01 5,56 ± 0,06 e 0,23 ± 0,08 0,59 ± 0,16 0,52 ± 0,22 Colloids of digested LBF in DIF are more stable and only split at the maximal concentration of 22 mM (Fig. 9a).Before that point, the size of the colloid grew, while the thickness of the vesicle wall thinned, as can be seen in the cross-sectional pictures in column (b) in Fig. 9. (The magenta-colored cremophor phase is a reference for comparing the thicknesses between the systems.)When the colloid splits in two, the new smaller colloids remain adjacent to each other.The total surface area of the colloids grows both due to the inner and outer surface expansion, as well as due to the split at the highest concentration.Blue points of glyceride-water contacts can be seen in column (c), both at the outer and inner surfaces of the vesicle shell and are easiest to see in the 16 mM system.Notably, the cremophor in two smaller colloids at 22 mM does not aggregate at the contact point of the vesicles, but rather resides at the opposite poles.
The number of contacts and SASA trends are presented quantitatively in Fig. 10.As can be seen in panel (a), the number of contacts between glycerides and water in undigested LBF micelle is lower than the contacts at the outer surface of digested LBF vesicle alone (except for simulation making use of 22 mM).The number of contacts at the inner surface takes nearly one-fifth of the total surface, whereas at the maximal BS concentration it takes more than one-third of the total N cont: G-W .In both digested and undigested LBF systems, the number of glyceride-water contacts decreases as the BS concentration increases up to 10 mM.After the split happens, the number of contacts with water increases in the undigested LBF system.
The number of contacts between the lipids and surfactant follows a similar trend in undigested LBF: first a reduction to 10 mM BS and then an increase.However, the difference between 16 mM and 22 mM is not significant.In the digested LBF, the number of contacts between cremophor and glycerides decreases as BS increases in the studied range.Nevertheless, the total number of glyceride-cremophor contacts is higher in vesicles (digested LBF) over the entire concentration range.
At the same time, the total area of the whole colloid is approximately the same, up to 10 mM BS (Fig. 10c).At higher concentrations, the splitting of colloids gives the undigested micelles a greater total area compared to the digested state vesicle.It is important to note that BS and PL were not considered for the total surface area calculation, as the free monomers would have contributed significantly to the standard deviation of the measurement.

Dog intestinal fluid colloids
The micelles formed in the simulation of DIF without LBF were small at the studied concentrations.The variability was high among the dogs, which could be a result the system size used in the simulations.Bigger simulation boxes could enable formation of bigger colloids, present in a lower number to correspond to the same concentration.The final configurations for the 3-microsecond simulations are presented in Fig. S4.Clearly, colloids formed in the simulations representing intestinal fluids Fig. 6.Radial distribution functions of molecules within colloids, including APIs.The core of the colloid is occupied by a mass of tri-and diglycerides in the undigested state and becomes filled with water molecules in the digested state (compare c,f, i to a,d,g and b,e,h).Redistribution from the surface of the colloid to a flatter distribution can also be seen for cremophor (b,e,h versus a,d,g).There is also a clear difference between a bimodal distribution of felodipine residing on both inner and outer water-vesicle interfaces and the narrow unimodal distribution of probucol in panels (f) and (i).The profiles were qualitatively very similar among the triplicate simulations, but we only present one example for each system to avoid averaging over distributions for colloids with varying eccentricity.Abbreviations: Carvcarvedilol, Felfelodipine, Probprobucol, CREcremophor, TGtriglycerides, DGdiglycerides, MGmonoglycerides, FFAfree fatty acids, BSbile salts, PLphospholipids.
in dogs 1 and 2, but the third dog simulation did not form a single colloid, most likely because the critical micelle concentration of the mix of surfactants and lipids was not reached.The radial distribution functions for pure DIFs and DIFs with a single drug molecule are presented in Fig. S5.Free fatty acids and phospholipids resided in the center of the colloid, whereas bile salts occupied the outer layers.Felodipine and carvedilol were partially present at the interface with water, whereas probucol was slightly more screened from the aqueous phase (Fig. S6, first column).As the number of drug molecules increased, the aggregate became rather like a cluster for all three APIs and was partially covered with DIF components (Fig. S6, columns 2-5).Surprisingly, even taurocholate molecules eventually left the aggregate surface in the felodipine and carvedilol simulation boxes.This was not the case for probucol, where the hydrophobicity of the API led to complete aggregation of all non-aqueous molecules.

Drug aggregation at various loadings
Apart from the mechanisms of colloidal transformation, we also wanted to estimate the drug solubility in the studied systems.From molecular simulation data, there is no trivial way to calculate solubility in complex media containing multiple molecules of different types.However, we applied two ways to estimate and compare solubility, at least qualitatively, with experimentally observed trends.The first approach was to vary the number of API molecules added to the simulation box.The average number of API-API contacts was counted in the systems for each of the three drugs at various loadings.If the number was below one, the drug molecules were considered to be well separated from each other, either within the colloid or in the bulk.If at least two molecules were in contact, this was taken as an indicator that the solubilization capacity of the medium was reached.We interpolated aggregation versus the number of drug molecules added to the system to the unity of API-API contacts number to determine this point.This was done for all three drugs under three different conditions: LBF in water (W in Fig. S7), undigested LBF in DIF (U), and digested LBF in DIF (D).No common trend for the three drugs was observed in the different media.Felodipine aggregated the least, but the critical aggregation concentration was approximately the same for all three media (Table S3).Probucol, a more hydrophobic API, aggregated at a significantly lower number of drug molecules.Carvedilol aggregated the most, specifically in the absence of bile and phospholipids.As observed from simulations, interactions between the drug molecules dominated despite seemingly equal affinity to the colloidal surface and to water.Variability among three different media was the highest among the drugs for carvedilol.Finally, there was no intersection with unity in the range of positive values, which is why no values for critical concentrations are given for it in Table S3.
This approach was not optimal given the amount of data produced in the current study and the high variability.Differences between the media were insignificant, and the observed trends did not match the experimental data.Even though the hydrophobicity and aggregation of probucol were reflected in the results, the differences for felodipine in different media and the highest solubility of carvedilol were not predicted correctly.

Solubility enhancement across methodologies
In the second approach to estimate solubility from MD simulations, we looked at the ratio between API contacts with micelle beads and water beads.The high contacts ratio was assumed to reflect the solubility enhancement of the API by the micelles.We were interested in the solubility enhancement over aqueous solubility, so we compared the simulation results to the ratio of measured solubility in the studied media over the aqueous solubility reported in the literature [52,53].These ratios for the three APIs followed a clear rank order: probucol, felodipine, then carvedilol (Fig. 11).This was observed in all simulated systems.Comparing this solubility ratio with the ratio of the contacts from our simulations, we saw that the rank order was the same for the APIs and that LBF in DIF was the preferable system for all APIs.This is in line with the experimental data for which DIF after administration of LBF had the highest solubility ratios.For probucol and felodipine, the simulated undigested system had a greater affinity to the APIs, whereas there was no clear difference between digested and undigested LBF for carvedilol.
When we compared the effect of the DIF molecules on the API solubility in the simulations, carvedilol showed a lower contact ratio if bile salts and phospholipids were not present in the LBF micelle.It is likely due to low affinity of carvedilol to cremophor that covered the surface of the LBF colloid prior to the addition of the DIF components (see Fig. 5a,b  and Figure7).For felodipine and probucol this was not as important; their contacts ratios were not as different between LBF in water and LBF in DIF.
In addition to the solubility measurements, we compared our findings with area under the curve (AUC) data from a previous in vivo study on dogs.The average AUC after administration of micronized carvedilol to three dogs was 1.23 and 1.38 times lower than that after administration of carvedilol pre-dissolved in LBF and drug co-administered with LBF, respectively [31].From our in vitro study, the solubility improvement in LBF + DIF was 5.48 times higher than in DIF alone for carvedilol, 1.77 times higher for felodipine, and 2.92 times higher for probucol.In silico, the addition of LBF to DIF increased solubility by factors of 3.82 for carvedilol, 3.89 for felodipine, and 2.42 for probucol.These comparisons, while not perfectly aligned in absolute values, qualitatively confirm a significant improvement in solubility due to the addition of LBF across all methodologies.

Discussion
In this study we demonstrated that solubilization patterns of poorly water-soluble drugs in LBF can be qualitatively, and to some extent quantitatively, predicted with computer modeling and with simulated intestinal fluids.The MD simulations showed, in most cases, the same trends as solubility data from literature and shake flask experiments.Thus, the in silico approach is valuable for evaluating the performance of formulation strategies.In particular, from in vitro and in silico Felodipine has the highest number of contacts with the surfactant (cremophor) and an intermediate number of contacts with water.Probucol is the most hydrophobic molecule, which is reflected by its number of contacts with water and the greater number of contacts with lipids and free fatty acids.Contacts with alike molecules were the most frequent for all APIs and were not presented on the graph.Interactions with ions were also omitted.Abbreviations: TGtriglycerides, DGdiglycerides, MGmonoglycerides, FFAfree fatty acids, CREcremophor, BSbile salts, PLphospholipids, Wwater.experiments we can see that a combination of the DIF components with LBF had greater potential than both LBF in water and DIF alone.We believe that the solubility of each API was similar in both DIF and LBF, as all three drugs can be well solubilized in BS-PL and lipidic aggregates.Then the difference in colloidal structures is less significant compared to the overall increased solubilization capacity provided by these colloids.
In the system containing both DIF and LBF, a synergistic effect is observed, where more drugs can be solubilized.We hypothesize that this is due to the increased overall mass of the colloids and the broader range of favorable interaction sites available around the larger and more complex colloidal structures.The consistency in solubility among all three drugs, as measured in vitro, despite differences in their physicochemical properties, such as logP, supports this hypothesis.High solubility enhancement for carvedilol in LBF in DIF was expected, since previous studies have shown that basic compounds [54] and specifically carvedilol [31], have a higher solubility when free fatty acid concentrations are elevated.Although our samples were taken from the earliest time point (5 min after administration), digestion had already released fatty acids (Table S4).The standard deviation was also high for carvedilol in DIF post-LBF consumption.We believe that it was mostly caused by interindividual difference, where one of the dogs had a solubility of 9.6 mg/mL, compared to the other two, (2.3 and 2.0 mg/ mL).Whether this divergence arises from differences in gastrointestinal motility or an irregular distribution of lipids in the water pockets of the small intestines where sampling took place is challenging to ascertain.This strong discrepancy was not seen for carvedilol solubility between dogs in the fluid samples after the administration of water (see table S5).Furthermore, as the same DIF was used for all drugs, the differences might also be related to individual variations in digestion capacity or patterns.Carvedilol, being a weakly basic drug, may be more sensitive to variations in acid release and digestive conditions, which could further explain the observed variability.
On the other hand, the solubilization enhancement in pure DIF samples was underestimated in the simulations, which might result from relatively low concentrations being used in small simulation boxes.In real dog intestinal fluids, the colloids might be bigger.Another limitation of the MD simulation is the size of the colloid itself that can be studied.Our DLS measurements on the undigested colloids ranged from 13 nm to 5 μm (Fig. S1).Our computational model was therefore representing a minor portion of the colloidal structures formed predominantly by LBF type IIIA-MC.However, in the digested state, the aggregates would most likely be at least 110 nm in diameter.The size of the simulation box necessary to introduce such colloids in MD would approach 120-130 nm in each direction to meet the minimum-image convention.The size is based on the assumption of a mostly spherical shape of the colloid, which is not necessarily the case as can be seen in Figs. 5, 9, and Table 4. Efficient (and sufficient) sampling in such large simulation boxes would take a very long time, even at the coarse-grained level of a Martini force field.Even coarser models could be introduced, but at the cost of accuracy.For these reasons, the current study simulated a smaller system that would reflect the reorganization of the same amount of LBF upon replacing TGs and DGs with MGs and FFAs.The pure DIF simulation showed that the drugs incorporated in intestinal fluid colloids only if the concentration of bile salts and phospholipids was sufficiently high, if the bile and phospholipids concentration is higher than the critical micelle concentration of the mixture.However, at the scale of tens of nanometers the aggregates formed by intestinal fluid components seemed to be rather too small to prevent the shielding of the drugs from each other (Fig. S6).Moreover, sodium taurocholate only seemed to have a high affinity to the probucol molecules, likely due to the high hydrophobicity of probucol.As for the micelle-water contact ratios, carvedilol seemed to have very low ratios in both pure DIF and pure LBF media, in agreement with the ratio of solubilization enhancement observed from the experimental data and literature.The ratios for probucol and felodipine in DIF were significantly lower than those in LBF.
Because of its capacity for examining solubilization mechanisms, MD has the potential to enable insights into ways of adjusting the composition of formulations.In this study we observed that the model is rather complex, as the drugs (for example, felodipine) may prefer to remain in contact with both surfactant and glycerides.On the one hand, the increase of bile concentration, at 16 mM and higher, might trigger split of the colloids.At the same time, the increase may lead to the surfactant being expelled from the surface of the colloid by the intestinal fluid components.The experimental study by Alskär et al. already showed that the amount of administered LBF affects the secretion of bile [31].By controlling the dose of the co-administered LBF or prandial state, one can potentially improve the drug solubilization.The BS concentration variation was referring to the values observed in three labrador dogs in the original study [31]; however, the range of BS and PL concentrations we simulated covers fasted and fed states in dogs and humans [31,55,56].It can then be used for further studies on optimal administration time relative to food intake.
Another interesting observation made with the MD simulations is about the morphological changes that colloids undergo upon digestion.Assuming that the model of 13-to 15-nm sized digested LBF colloid is valid, the micelle observed in the undigested state is transformed into a vesicle in the digested state.This transformation results in more felodipine molecules that can reside at energetically favorable places (comparing the number of contacts with water in undigested and digested states for felodipine in Fig. 7).As we discovered, the main mechanism leading to this is an increase in the surface area due to the appearance of the inner lipids-water interface and an expansion of the entire colloid.
RDF diagrams (Fig. 6) can assist in quantitative analysis and comparison of drug placement in the colloids.One potential application could be the comparison of various formulation compositions at different degrees of digestion.A broader spectrum of intermediate steps in digestion, mimicking the dynamics of the morphological changes, could be introduced in MD via gradual replacement of the triglycerides and diglycerides in contact with the aqueous phase.This knowledge could be used in timing the optimal release of the drugs with various excipients.Williams et al reported that a concentration of bile salts above 3 mM might not dramatically improve danazol solubility in LBF types IIIA and IIIB [57].From the perspective of our study, however, this behavior is perhaps not universal for all poorly water-soluble drugs.Felodipine has a similar molecular weight as danazol, is also neutral, and has a similar logP (4 versus 3.8 of danazol), but it places itself preferentially next to the colloid-water interface.For drugs like this, an increased bile concentration is beneficial because it increases energetically favorable space within the colloid.
The computational model looks very promising from a 3R perspective because of the good agreement between the drug solubility in dog FaSSIF and DIF samples.However, there are certain limitations.As reported by Kalantzi et al., the solubility of weakly basic molecules, in both canine intestinal fluids and FaSSIF, predicts human intraluminal solubility, but only for the fasted state [56].Discrepancies with fed state solubility could reach up to 40% with the increased concentration of bile salts in dogs.In the experimental part of the current study, the weakly basic carvediol had the highest variability, as bile concentration did indeed vary greatly in the samples.
Our study aimed to bridge in vitro and in silico methodologies with in vivo relevance.To this end, we compared the solubility improvements observed in our experiments with the AUC data from a previous in vivo study.While the quantitative differences for carvedilol across methodologies are not perfectly aligned, they qualitatively confirm the significant solubility enhancement provided by LBF addition.This highlights the potential of combining in vitro and in silico methods to predict and understand in vivo behaviors, thereby supporting the use of these approaches as valuable prescreening tools in drug development.
The affordability of the computational experiments and total control over the studied environment can reduce the number of laboratory experiments, including those involving animals.Apart from dog studies in the preclinical stage for human drugs, many others are done to develop medicines and drug delivery systems for animal treatment [58][59][60].Therefore, for multiple reasons, it is crucial to develop protocols for computer simulations that predict the performance of active pharmaceutical ingredients.As we have shown here, the trends of improving solubility with various LBFs could be predicted computationally and experimentally using FaSSIF.This combination of in silico and in vitro approaches can thus reduce the number of studies on animals.

Conclusion
The solubilities of carvedilol, probucol, and felodipine were experimentally measured in DIF and LBF samples.Computational models of DIF and LBF were introduced and the solubilization patterns of the drug molecules in different media were studied.The computational analysis proved to be in qualitative agreement with the experimental data.Synergistic effects were observed for intestinal fluid and LBF components, which together efficiently solubilized the drug molecules.The MD simulations of the three compounds showed different preferences in the molecular interactions with the components within the colloidal structure.MD simulations suggested that accurately adjusting the surfactantlipids ratio could be important in optimizing LBF for improved drug release and absorption in the small intestine.We observed splitting of the colloids with increased bile salt concentration and also saw the transformation of a micelle to a vesicle as triglycerides and diglycerides were replaced with monoglycerides and free fatty acids to mimic the digestion process.The solubility of the three drugs in dog FaSSIF and real DIF samples did not differ significantly from each other.We believe that combining in silico and in vitro experiments based on simulated intestinal fluids, can become a reasonable substitution for many prescreening tests and experiments requiring biological fluids samples from animals.

Fig. 2 .
Fig. 2. The computationally simulated systems.(a) The three categories of colloids in this study: lipid-based formulation (LBF) dispersed in water; undigested LBF with added bile salts (BS) and phospholipids (PL) representing dog intestinal fluid (DIF); and digested LBF in DIF.Triglycerides (TG) and diglycerides (DG) were replaced by monoglycerides (MG) and free fatty acids (FFA) in the latter.Pure DIF colloids are not shown here.(b) Snapshots representing the dimensions of the simulation boxes used for pure DIF and LBF/LBF + DIF systems.a is the cubic box size, ⌀ is the average diameter of the aggregates (given here as a reference; specific values can be found in the Table4).

Fig. 4 .
Fig. 4. Comparison of drug solubility in dog intestinal fluid (DIF) samples and in dog Fasted State Simulated Intestinal Fluid (FaSSIF), with and without lipidbased formulations (LBF,) and in pure LBF in water.The differences between DIF and corresponding dog FaSSIF values are insignificant for all drugs and both in the presence and absence of LBF.(** p < 0.005, *** p < 0.0002).All experiments were done in triplicates.

Fig. 5 .
Fig. 5. Assembled colloids from simulations of felodipine in lipid-based formulations (LBF) and dog intestinal fluid (DIF).Vertical slices of the middle part of the colloids are shown; water is omitted for clarity.a) LBF in water formed a spherical colloid with a nearly uniform distribution of surfactant across the surface of the lipids.b) Upon digestion of the bile salts and phospholipids, most of the surfactant was pushed out by the newly added molecules to one pole of the colloid.c) The micelle transformed into a vesicle after replacing tri-and diglycerides with monoglycerides and free fatty acids.Abbreviations: TGtriglycerides, DGdiglycerides, MGmonoglycerides, FFAfree fatty acids, CREcremophor, BSbile salts, PLphospholipids, APIactive pharmaceutical ingredient.

Fig. 7 .
Fig. 7. Distribution of contacts for APIs with molecules of other types during the last 3 μs, presented as a portion of all API contacts with other molecules.W, Ud and D on the left from the bars stand for the systems with LBF in water, undigested LBF in DIF, and digested LBF in DIF, respectively.Carvedilol clearly interacts mostly with water molecules and components of the intestinal fluid.Felodipine has the highest number of contacts with the surfactant (cremophor) and an intermediate number of contacts with water.Probucol is the most hydrophobic molecule, which is reflected by its number of contacts with water and the greater number of contacts with lipids and free fatty acids.Contacts with alike molecules were the most frequent for all APIs and were not presented on the graph.Interactions with ions were also omitted.Abbreviations: TGtriglycerides, DGdiglycerides, MGmonoglycerides, FFAfree fatty acids, CREcremophor, BSbile salts, PLphospholipids, Wwater.

Fig. 8 .Fig. 9 .
Fig. 8. Morphological changes in undigested LBF colloids upon adding different amounts of bile salts and phospholipids.a) General view on the colloids in VMD, color-coded to demonstrate the molecule distribution.b) and c) The surfactant and glyceride parts of the colloid split and are depicted as solvent-accessible surface area.Grey dots in column (b) show the contacts with water, orange dots in column (c) show the surface of the glycerides available for bile salts, phospholipids, water and ions, and the green dots depict the interface surface between the surfactant and lipids.In column (d) only glycerides and their contact points with water molecules (depicted as blue dots) are shown.Abbreviations as in Fig. 7, except GLY standing for glycerides (TG, DG and MG).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10 .Fig. 11 .
Fig.10.Contact areas between different molecule types present in the simulation boxes and measured as the number of solvent probes with a radius of 0.14 nm fitting at the interface.a) The trend in aqueous lipids contacts for digested LBF system is simpler than that for the undigested due to fewer splits of the colloids as the bile salts increase.b) Number of contacts between the surfactant (cremophor -CRE) and glycerides (G) is higher in digested LBF in DIF than in undigested in DIF for all concentrations (except the one without added bile salts).c) Total area of the glyceride-surfactant core.

Table 1
Simulations in this study.

Table 2
Composition of dog intestinal fluid models in MD simulations.

Table 3
Composition of LBF and LBF + DIF systems in MD simulations.