A. A. Anosov

PEG blocking of single pores arising on phase transitions in unmodified lipid bilayers

Changes in ionic permeability of bilayer lipid membranes (BLM) from dipalmitoyl phosphatidylcholine at temperature of phase transition in 1 M LiCl solution in the presence of polyethyleneglycols (PEG) of various molecular masses are studied. The transition of ionic membrane channels from conducting to blocked nonconducting state using polymers makes it possible to calibrate lipid pores. It is shown that low-molecular weight glycerol and PEG with molecular weights of 300 and 600 decrease the amplitude of current fluctuations through the membrane, the decrease being proportional to the size of the polymer molecule incorporated. The addition of PEG with molecular masses of 1450, 2000, and 3350 decrease the current fluctuations to the basal noise level. The result is considered as a complete blockade of ion channel conductivity. In the presence of rather large polymers, such as PEG with molecular masses of 6000 and 20000, which are hardly incorporated in the pore, single current fluctuations occur again; however, their amplitudes are somewhat smaller than in the absence of PEG. It is assumed that a complete blockade of the conductivity of lipid ionic channels by PEG with molecular masses of 1450, 2000, and 3350 is due to dehydration of the pore gap and the conversion of the hydrophilic pore to a hydrophobic one.

States of lipid pores in bilayer lipid membranes at a phase transition in a LiCl solution with addition of molecules of polyethylene glycol

Statistics of times of open and closed states of lipid pores in planar lipid bilayer membranes that consisted of dipalmitoylphosphatidyl choline were experimentally studied at a temperature of a phase transition in the 1 M solution of LiCl after the addition of water-soluble molecules of polyethylene glycol of different molecular masses. Transmembrane current impulses were measured in a voltage-clamp regime (50 mV). Histograms of the impulse duration and impulse intervals had a non-exponential shape and a pronounced characteristic maximum. Therefore, the sequence of impulses of the transmembrane current under the conditions of phase transition was dependent. New impulses appeared depending on the time of antecedent impulses, and the moment of the impulse completion depended on the moment of its start. The proposed Erlang model quite accurately approximated the experimental histograms. According to this model, a lipid pore had several open and closed states.

Acoustic thermometric reconstruction of a time-varying temperature profile

The time-varying temperature profiles were reconstructed in an experiment using a thermal acoustic radiation receiving array containing 14 sensors. The temperature was recovered by performing similar experiments using plasticine, as well as in vivo with a human hand. Plasticine preliminarily heated up to 36.5°C and a human hand were placed into water for 50 s at a temperature of 20°C. The core temperature of the plasticine was independently measured using thermocouples. The spatial resolution of the reconstruction in the lateral direction was determined by the distance between neighboring sensors and was equal to10 mm; the averaging time was 10 s. The error in reconstructing the core temperature determined in the experiment with plasticine was 0.5 K. The core temperature of the hand changed with time (in 50 s it decreased from 35 to 34°C) and space (the mean square deviation was 1.5 K). The experiment with the hand revealed that multichannel detection of thermal acoustic radiation using a compact 45 × 36 mm array to reconstruct the temperature profile could be performed during medical procedures.

Bilayer permeability during phase transition as an Erlang flow of hydrophilic pores resulting from diffusion in the radius space

The formation of hydrophilic pores in a lipid bilayer during phase transition is described using the Smoluchowski equation with an additional term of the hydrophobic pore source. This term is added to account for defects in lipid packing during phase transition. We assume that the temporal sequence of the pores is a stochastic process, a non-stationary second-order Erlang flow. Flow characteristics depend on the equation solution and determine the formation times of the hydrophilic pores. The calculated distribution of the durations of intervals between hydrophilic pores is in a good agreement with experimental data published before. In the context of this model we describe the influence of poly(ethylene glycol) on the pore formation frequency.

Application of the Smoluchowski equation with a source term to the model of lipid pore formation during a phase transition

The Smoluchowski equation, which describes pore diffusion in the radius space, with a source term, is used in modeling the process of the formation of a hydrophilic pore in a lipid bilayer during phase transition. The introduction of a hydrophobic-pore source term into the equation reflects the emergence of additional defects in a bilayer caused by the decrease in the molecule area under the transition from the liquid crystalline to the gel phase. The distribution of the time probability density calculated within the model that is required for the formation of a hydrophilic pore is in good agreement with the previously published experimental data.

Instrument function of a broadband acoustic thermometric detector

The instrument function of a broadband (1.6–2.5 MHz) detector that is used in acoustic thermometry has been calculated. Experimental tests have proved that measured and computed results are in agreement. The effect of the pass band characteristics and the detector’s dimension on the instrument function has been studied as well as the effect that the instrument function has on an acoustic thermometric signal that is measured by the detector. The ratio of the wavelength (for the mean reception frequency) to the detector’s radius has been shown to be the main parameter that determines the acoustic thermometric signal at distances that are typical of acoustic thermometry. For problems of localizing a heated domain, it is optimal to locate the receiver at a distance of 15–25 mm from the domain. For example, for a detector 8 mm in diameter, the width of the instrument function at a level of 0.5 of the maximum is 1.2 ± 0.1 mm in this zone.

Possibilities of acoustic thermometry for controlling targeted drug delivery

Model acoustic thermometry experiments were conducted during heating of an aqueous liposome suspension. Heating was done to achieve the liposome phase transition temperature. At the moment of the phase transition, the thermal acoustic signal achieved a maximum and decreased, despite continued heating. During subsequent cooling of the suspension, when lipids again passed through the phase transition point, the thermal acoustic signal again increased, despite a reduction in temperature. This effect is related to an increase in ultrasound absorption by the liposome suspension at the moment of the lipid phase transition. The result shows that acoustic thermography can be used to control targeted delivery of drugs mixed in thermally sensitive liposomes, the integrity of which is violated during heating to the phase transition temperature.

Erlang flow of hydrophilic pore formation and closure events in a lipid bilayer during phase transition resulting from diffusion in the radius space

The Smoluchowski equation with an energy profile of a special type and an assumed hydrophobic (“half”) pore source term is used to describe the process of hydrophilic pore formation in a lipid bilayer at the gel-liquid phase transition. The source term reflects the occurrence of molecule packing defects in a lipid bilayer at phase transition. The time sequences of the pore formation and closure events are treated as non-stationary, second-order Erlang flows whose characteristics depend on the equation solution. The computed distributions of the time intervals between hydrophilic pores, and pore lifetimes agree with the previously published experimental interpulse interval and pulse duration histograms for the current fluctuations through planar bilayer membranes of DPPC immersed in a LiCl aqueous solution containing polyethylene glycol. Thus, the statistical analysis of pore formation and closure times leads us to conclude that firstly, the increased permeability of a lipid bilayer during the gel-liquid phase transition is accounted for by the emergence of additional hydrophobic defects in the heterogeneous structure of the bilayer and secondly, that the non-exponential distributions of the lipid channel closed and open times observed in experiments are evidence that the process of hydrophilic pore formation is not a one-step process but involves at least two dependent events.

Acoustothermography: Correlation and noncorrelation methods

The correlation and noncorrelation methods for the reception of thermal acoustic radiation are tested experimentally. For the correlation reception, a formula is obtained for calculating the temperature distribution of an object from the measured crosscorrelation pressure functions of thermal acoustic radiation. Noncorrelation measurements with the use of two mutually perpendicular planar arrays, each consisting of seven sensors, have made it possible to determine the parameters of the 3D temperature distribution. The measurement duration is 10 s.