Pharmacokinetic Modeling of Morphine's Effect on Plasma Concentrations of Ticagrelor and Its Metabolite in Healthy Volunteers.

This study aimed to build a mathematical model describing the pharmacokinetics of ticagrelor and its active metabolite (AR-C124910XX) in a stable setting with concomitant administration of morphine. The model consists of a set of four differential equations prepared upon the available knowledge regarding the biological processes in the pharmacokinetics of ticagrelor. The set of equations was solved numerically using the Runge-Kutta method. The data were obtained in a double-blind, randomized, placebo-controlled, crossover trial. Twenty-four healthy volunteers received a 180-mg ticagrelor loading dose together with either 5-mg morphine or placebo. Blood samples were analyzed with liquid chromatography-tandem mass spectrometry to assess plasma concentrations of ticagrelor and AR-C124910XX before ticagrelor loading dose and after that 1, 2, 3, 4, and 6 h. The model allowed us to reproduce the experimental results accurately and led us to conclusions consistent with clinical observations that morphine delays the time of maximum drug concentration and that the morphine effect occurs due to decreased gastrointestinal motility. Based on the model, we were able to predict the effect of drug dose on receptor blocking efficacy.

A computer study of the risk of cholesterol gallstone associated with obesity and normal weight.

Obese people differ from the people of normal weight in gall bladder motility and have a higher risk of cholesterol stone formation. In this study, using a mathematical model of cholesterol homeostasis, which also considers the enterohepatic circulation of bile as well as cholesterol, we investigated the risk of cholesterol stone formation in obese and normal-weight groups who had normal blood cholesterol levels. We associated the risk of stone formation with the amount of cholesterol released into bile and the amount of de novo-synthesized cholic acid. For both groups, we determined the conditions of low and high risk. In addition, we analyzed the potential effects of changes in gall bladder motility with increased weight. The results showed that the obese group exhibited increased kinetics of enterohepatic circulation, leading to a significant increase in blood cholesterol levels, which can be reduced by increasing the amount of cholesterol in bile. Based on this finding, we suggest that for obese people, it is beneficial to reduce the amount and change the composition of circulating bile through the inhibition of cholic acid synthesis along with cholesterol synthesis. Furthermore, obese people should maintain a triglyceride-lowering diet and consume small meals containing fat, preferably in combination with agents that can reduce bile output from the gall bladder.

A model of lipid rearrangements during pore formation in the DPPC lipid bilayer.

CONTEXT: The molecular bases of pore formation in the lipid bilayer remain unclear, as do the exact characteristics of their sizes and distributions. To understand this process, numerous studies have been performed on model lipid membranes including cell-sized giant unilamellar vesicles (GUV). The effect of an electric field on DPPC GUV depends on the lipid membrane state: in the liquid crystalline phase the created pores have a cylinder-like shape, whereas in the gel phase a crack has been observed. OBJECTIVE: The aim of the study was to investigate the geometry of pores created in a lipid bilayer in gel and liquid crystalline phases in reference to literature experimental data. METHODS: A mathematical model of the pore in a DPPC lipid bilayer developed based on the law of conservation of mass and the assumption of constant volume of lipid molecules, independent of their conformation, allows for analysis of pore shape and accompanying molecular rearrangements. RESULTS: The membrane area occupied by the pore of a cylinder-like shape is greater than the membrane area occupied by lipid molecules creating the pore structure (before pore appearance). Creation of such pores requires more space, which can be achieved by conformational changes of lipid chains toward a more compact state. This process is impossible for a membrane in the most compact, gel phase. DISCUSSION AND CONCLUSIONS: We show that the geometry of the pores formed in the lipid bilayer in the gel phase must be different from the cylinder shape formed in the lipid bilayer in a liquid crystalline state, confirming experimental studies. Furthermore, we characterize the occurrence of the 'buffer' zone surrounding pores in the liquid crystalline phase as a mechanism of separation of neighbouring pores.

Two-compartment model as a teaching tool for cholesterol homeostasis.

Cholesterol is a vital structural and functional molecule in the human body that is only slightly soluble in water and therefore does not easily travels by itself in the bloodstream. To enable cholesterol's targeted delivery to cells and tissues, it is encapsulated by different fractions of lipoproteins, complex particles containing both proteins and lipids. Maintaining cholesterol homeostasis is a highly regulated process with multiple factors acting at both molecular and tissue levels. Furthermore, to regulate the circulatory transport of cholesterol in lipoproteins, the amount of cholesterol present depends on and is controlled by cholesterol dietary intake, de novo synthesis, usage, and excretion; abnormal and/or unbalanced cholesterol levels have been shown to lead to severe outcomes, e.g., cardiovascular diseases. To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis. Using the model and a hands-on approach, students can familiarize themselves with the basic components and mechanisms behind balanced cholesterol circulatory transport as well as investigate the consequences of and countermeasures to abnormal cholesterol levels. Among others, various treatments of high blood cholesterol levels can be simulated, e.g., with commonly prescribed de novo cholesterol synthesis inhibitors.

Membrane fluidity and the surface properties of the lipid bilayer: ESR experiment and computer simulation.

Penetration of the liposome membranes formed in the gel phase from DPPC (DPPC liposomes) and in the liquid-crystalline phase from egg yolk lecithin (EYL liposomes) by the TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl) and 16 DOXYL (2-ethyl-2-(15-methoxy-oxopentadecyl)-4,4-dimethyl-3-oxazolidinyloxy) spin probes has been investigated. The penetration process was followed by 120 hours at 24(0)C, using the electron spin resonance (ESR) method. The investigation of the kinetics of the TEMPO probe building into the membranes of both types of liposomes revealed differences appearing 30 minutes after the start of the experiment. The number of TEMPO particles built into the EYL liposome membranes began to clearly rise, aiming asymptotically to a constant value after about 100 minutes, whereas the number of the TEMPO particles built into the DPPC liposome membranes was almost constant in time. The interpretation of the obtained experimental results was enriched with those of computer simulation, following the behavior of the polar heads (dipoles) of the lipid particles forming a lipid layer due to the change in the value of the model parameter, k, determining the mobility of the dipoles. The possibility of the formation of an irregular ordering of the polar part of lipid membranes was proved, which leads to the appearance of spaces filled with of water for k > 0.4. The appearance of these defects enables the penetration of the bilayer by the TEMPO particles. The limited mobility of lipid polar heads (k < 0.2) prevents the appearance of such areas facilitating the penetration of the lipid membrane by alien particles in the gel phase.

A pore creation in a triangular network model membrane.

Membrane electroporation seems to be a useful method for delivery of biological active compounds into the cell. Although it is known that this phenomenon is sensitive to the electric field intensity, duration of the electric pulse and its shape, it is not fully understood. In some theoretical descriptions it is postulated that a hydrophobic pore appears at an early stage of pore creation. Here we show how to construct a hydrophilic pore structure connecting two parallel triangular networks modeling lipid membrane. It would be useful in Monte Carlo simulation studies on electroporation. In our model the pore appearance requires only movement of one lipid molecule. At the same time the chains of the second lipid molecule should occupy two nodes, one in each network to compensate the differences in chain packing densities when electric field is applied. In consequence the hydrated polar head should be placed in a hydrophobic part of the membrane giving rise to the hydrophilic pore. We also discuss the relation between the pore diameter and its shape.

Modeling the induction of lipid membrane electropermeabilization.

Experiments show significant effects of an electric field on lipid membrane, leading to a pore formation when a high intensity field is applied. The phenomenon of electroporation is preceded by the induction and expansion of defects, responsible for the pre-pore excitation. We examine the mechanism of the induction of the field-driven defects by Monte Carlo simulations. The study is based on the improved Pink's model, which includes explicit interactions between the polar heads and energy of interactions between the heads and the field. No anomalous deformation of the molecules is considered. The study, provided for bilayer dipalmitoyl-phosphatidylcholine (DPPC) membrane in the gel (300 K) and fluid (330 K) phases, shows dependence of the membrane conformational and energetical state on the value of the electric field. We observe that the electric field affects the number of molecules in the gel and in the fluid states. In the layer at the negative potential, when the transmembrane voltage is above U(c) approximately 280 mV, lipid heads abruptly reorient and the number of local spots with fluid conformation increases. The other layer slightly tends to tighten its structure, producing additional mechanical stress between layers. Lipids showed complete insensitivity to the electric field within physiological limits, U<70 mV.

Simulation of electroporated cell by chronopotentiometry.

Chronopotentiometry on planar lipid bilayer (BLM) is proposed as a method for modeling the electrical phenomena in electroporated cell. Two techniques are discussed: constant-current and linear-current chronopotentiometry. It is proposed that the constant-current chronopotentiometry may provide basis for modeling the electroporated cell shortly after the removal of the electric field, when activity of cellular pumps counteracts ionic fluxes through the electropore and ionic channels. The linear-current method can be considered for modeling the cell in the later stage after electroporation, when energetical resources of the cell are gradually getting exhausted and the activity of pumps decreases. Based on this idea, it may be postulated that the electropore in the cell has fluctuating dynamics whose stochastic characteristics, similarly as biological channels, shows 1/f noise. The model implies that the fluctuations would disappear leaving the electropore with a constant resistance when efficiency of the pumps becomes very small. The results of chronopotentiometry also may suggest that opening time, conductivity and selectivity of the electropore can be controlled by the cell environment or membrane composition.

Structural and energetic model of the mechanisms for reduced self-diffusion in a lipid bilayer with increasing ionic strength.

Ionic concentration of the buffer strongly affects properties of a lipid membrane, such as membrane durability (e.g., in electroporation experiments), lateral diffusion coefficient, and zeta potential. The effect of ionic strength is studied by Monte Carlo simulations based on the improved Pink model with explicitly included interactions between lipid heads. We examine the energetic profile of the membrane, conformation of lipid molecules, and molecular interactions. The study is provided for dipalmitoyl-phosphatidylcholine (DPPC) membrane in the gel (300 K) and fluid (330 K) temperatures for the ionic strength in the range 10-3000 mM at several values of dielectric constant. At high ionic strength, the simulations indicate an increase of the membrane stability due to the screening of the repulsive forces between lipid heads, more stable conformation of lipid chains, and denser packing of the molecules. These effects may account for reduced lateral diffusion in the membrane, as observed in experiments. The simulation also suggests that chains tend to assume a more straightened configuration and the number of standing polar heads increases, which may contribute to thickening of the membrane. An increase of the head tilt dependent on ionic strength may account for the greater value of zeta potential. The model shows stronger electropermebilization of the membrane in external electric field when ionic strength is low.

The dependence of Fluorescein-PE fluorescence intensity on lipid bilayer state. Evaluating the interaction between the probe and lipid molecules.

The degree of dependence of a lipid bilayer's surface properties on its conformational state is still an unresolved question. Surface properties are functions of molecular organization in the complex interfacial region. In the past, they were frequently measured using fluorescence spectroscopy. Since a fluorescent probe provides information on its local environment, there is a need to estimate the effect caused by the probe itself. In this paper, we address this question by calculating how lipid head-group orientation effects the fluorescence intensity of Fluorescein-PE (a probe that is sensitive to surface potential). In the theoretical model assumed the lipid bilayer state and the interactions between the charged fluorescent probe and the surrounding lipid molecules was evaluated. The results of this theoretical analysis were compared with experimentally obtained data. A lipid bilayer formed from DPPC was chosen as the experimental system, since it exhibits all the major conformational states within a narrow temperature range of 30 degrees C-45 degrees C. Fluorescein-PE fluorescence intensity depends on local pH, which in turn is sensitive to local electrostatic potential in the probe's vicinity. This local electrostatic potential is generated by lipid head-group dipole orientation. We have shown that the effect of the probe on lipid bilayer properties is limited when the lipid bilayer is in the gel phase, whereas it is more pronounced when the membrane is liquid-crystalline. This implies that Fluorescein-PE is a good reporter of local electrostatic fields when the lipid bilayer is in the gel phase, and is a poor reporter when the membrane is in the liquid-crystalline state.

Computer simulation studies on significance of lipid polar head orientation.

Models of lipid bilayer were extended and dipole structure of polar head in lipid molecules was included. As a result a wavy structure, resembling experimentally observed 'ripple phase', was obtained. The discussion on significance of interactions between dipoles that constitute polar part of the model membrane is presented. Assumptions of the model are closer to the real conditions and reflect the real phenomena much better. Dependence of the model system behaviour on dielectric permeability, ionic strength, and temperature was studied. An influence of reduced number of freedom degrees in the dipole system on the membrane properties was also considered. It was proved that if dielectric permeability of membrane polar part is significantly smaller than water dielectric permeability then the membrane model does not have to take into account changeability of dipole tilt towards membrane surface. This assumption becomes more significant for dielectric permeability epsilon approaching epsilon = 80. Packing degree of hydrocarbon chains in hydrophobic part of the membrane is also responsible for the angle value between dipoles and the membrane surface. The model results are compared to experimental results obtained by means of fluorescence probe fluorescein-PE.

Computer simulation studies on the significance of lipid polar head charge.

Ripple phase modelling was achievable by taking into consideration the dipole structure of the polar heads of model membrane molecules. Computer simulations enabled the selective analysis of a model membrane. Considering only the hydrophobic part of the lipid membrane, the gel-fluid transition stage can be obtained in such a simulation. Assuming an additional degree of freedom, the entire molecule can move along the normal to the membrane surface projected from two C-C bonds. The amounts of shifted lipids were 17% and 33% at temperatures of 300 K (gel) and 330 K (fluid), respectively. Taking into account only polar head interactions in media of different ionic strength I, dielectric constant epsilon, and an effective charge and temperature, we could observe the same behaviour of the examined system independently of the values of I and ( when the charge was reduced to q/2. The amount of shifted heads at 300 K decreases sharply with the reduced charge value, with an accompanying increase in the number of "standing" polar heads. Summing up, it can be stated that hydrocarbon lipid chains exhibit a greater tendency to displacement in the fluid state than in the gel state. However, the polar heads behave in the opposite way: there are more displaced heads at 300 K than at 330 K. Thus, the overall analysis of the interactions between the molecules of the model membrane should enable us to find model parameters suitable for studying the lipid membrane at a wide range of temperatures. Finally, an electrostatic profile close to the membrane surface could be estimated in different membrane states. This should be useful in membrane-biologically active compound interaction analysis.