Elsevier

Biosystems

Volume 102, Issues 2–3, November–December 2010, Pages 134-147
Biosystems

Diffusion–convection effects on drug distribution at the cell membrane level in a patch-clamp setup

https://doi.org/10.1016/j.biosystems.2010.09.003Get rights and content

Abstract

We present a model-based method for estimating the effective concentration of the active drug applied by a pressure pulse to an individual cell in a patch-clamp setup, which could be of practical use in the analysis of ligand-induced whole-cell currents recorded in patch-clamp experiments. Our modelling results outline several important factors which may be involved in the high variability of the electric response of the cells, and indicate that with a pressure pulse duration of 1 s and diameter of the perfusion tip of 600 μm, elevated amounts of drug can accumulate locally between the pipette tip and the cell. Hence, the effective agonist concentration at the cell membrane level can be consistently higher than the initial concentration inside the perfusion tubes. We performed finite-difference and finite-element simulations to investigate the diffusion/convection effects on the agonist distribution on the cell membrane. Our model can explain the delay between the commencement of acetylcholine application and the onset of the whole-cell current that we recorded on human rhabdomyosarcoma TE671 cells, and reproduce quantitatively the decrease of signal latency with the concentration of agonist in the pipette. Results also show that not only the geometry of the bath chamber and pipette tip, but also the transport parameters of the diffusive and convective phenomena in the bath solution are determinant for the amplitude and kinetics of the recorded currents and have to be accounted for when analyzing patch-clamp data.

Introduction

Diffusive–convective bio-transport can play an important role in a number of processes with physiological and clinical relevance. For instance, exocytotic release of neurotransmitters such as adrenaline or serotonin from granules or vesicles can be accompanied by convection associated with both the extracellular bulk flow and the dilution of the granule matrix due to fast swelling (Fan and Fedorov, 2004). New methods of convection-enhanced drug delivery (Sawyer et al., 2006, Oh et al., 2007) were developed recently to deliver compounds throughout the brain by applying an external pressure gradient to induce fluid convection in the brain via a small catheter with an internal diameter of about 1 mm. This flexible technique which allows dosing of large areas of tissue and concentrating the infusate in situ can be used in chemotherapy for intratumoral drug administration (e.g., inside gliomas), as well as in gene therapy or immune therapy. However, although, the method has been proven to be generally reproducible and clinically safe, unpredictable fluid flow may arise due to the complex anatomy of the brain which can lead to collection of the drug in the perivascular spaces and cause incidences of edema (Sawyer et al., 2006), which points to the need for detailed quantitative models of drug transport via diffusive-convective processes inside the brain tissue (Sarntinoranont et al., 2006, Linninger et al., 2008, Smith and García, 2009). Several complications of the problem arise from the variable contribution at a microscopic scale of geometric and viscous factors that may affect mass transport, such as the molecular composition of the extracellular medium, tissue porosity and connectivity between fluid-filled spaces, or the presence of macromolecular obstacles which can retard diffusion and contribute to the characteristic tortuosity of the nervous tissue (Rusakov and Kullmann, 1998, Syková and Nicholson, 2008). Nevertheless, the biophysical issues are complex and not fully resolved at the moment. A similar principle is involved in the technique of microdyalisis, which has been widely used to measure acetylcholine (ACh) release in vivo and has revealed the effects of psychoactive and therapeutic drugs on cholinergic transmission (Bruno et al., 2006). In this procedure a micropipette with an inner radius of ∼10 μm is used to deliver ACh or other probing solutions via pressure ejection directly into the brain tissue, and specific microelectrode devices are used to probe the ensuing response at a distance of several hundreds of micrometers away from the micropipette (Bruno et al., 2006, Syková and Nicholson, 2008).

Pressure-controlled ejection through the tip of a micropipette is also a common method for agonist delivery to individual cells in patch-clamp measurements. The patch-clamp method (Hamill et al., 1981) is one of the most widely used electrophysiological techniques for studying both voltage-activated and ligand-activated (such as ionotropic receptors) membrane ionic channels. When ionotropic membrane receptors are studied by the patch-clamp technique, the agonist is applied by pressure through a perfusion system where the flow of the active solution is controlled via a group of pinch valves, and the flow velocity depends on the pressure of the air communicating with the drug containers (Fig. 1). The effective amount of the drug interacting with the membrane receptors of a studied cell depends, under these conditions, on the drug concentration in the application containers (which is readily controllable by the experimenter), but also depends on other additional parameters of the patch-clamp setup. Such parameters are: the perfusion pressure, the mobility of the drug in the bath solution, as well as geometrical parameters such as the diameter of the perfusion tubes, the distance between the cell and the tip of the perfusion system, or the size of the cell. The studies of Lisk and Desay (2006) on red blood cells have indicated that the perfusion parameters critically affect the quality of the seal, and underlined that perfusion artefacts can impair the quality of the electrophysiological recordings. Di Angelantonio and Nistri (2001) found that short pressure pulses (10–50 ms) and agonist concentrations in the range 20–100 μM produce linear responses in the same cells. Using diffusion equations for a continuous point source, they calculated that the amount of agonist (nicotine in their study) undergoes limited dilution in the extracellular microenvironment under their experimental conditions.

To the best of our knowledge, there are no quantitative models on the kinetics of drug distribution at the cell membrane level in specified patch-clamp setups based on pressure-controlled ejection of the agonist in the extracellular bath solution. Our study focuses on the particular case of acetylcholine (ACh) application to evoke whole-cell currents on human rhabdomyosarcoma TE671 cells, which express nicotinic acetylcholine receptors (nAChR) on the plasma membrane. The influence of geometric parameters of the environment on the amount of acetylcholine that stimulates postsynaptic nicotinic receptors has been studied for in vivo situations (Whatey et al., 1979, Khanin et al., 1994, Smart and McCammon, 1998, Tai et al., 2003, Popescu and Morega, 2004). However, in most patch-clamp studies the authors generally present the particular conditions of their own setups, making the comparison between the results of different studies quite difficult. Taking into account the different perfusion conditions and different shapes/dimensions of the perfusion chambers and pipette tips could provide a consistent background for such a comparison. In this paper, we present a modelling study on the effects of the geometry and flow parameters on the actual amount of agonist that reaches the cell membrane, with the aim of determining the optimal experimental conditions required for studying ligand–receptor interactions by the patch-clamp technique, as well as to provide possible corrections to be accounted for when interpreting the patch-clamp data.

In our model, we consider that the transport of the neuroactive drug (acetylcholine here) to a relatively close cell is determined by diffusive and convective processes. The release source is realistically modelled as being distributed over the surface of the pipette tip (with a diameter of 600 μm), and the duration of the pressure pulse (1 s) is longer than in previous studies (Di Angelantonio and Nistri, 2001). We used two different numerical methods (a finite difference and a finite element method, respectively) to solve the transport equations in the computation domain, and the agreement between the results obtained with the two methods was good. To increase the computation speed, we modelled the decay of the flow velocity with the distance from the tip as an exponential function, which is supported by classical theory of the “submerged jet” of fluid ejected from a point source or from a cylindrical tube into an unconfined space filled with the same fluid. Complex computational models incorporating data provided by magnetic resonance microscopy and diffusion tensor imaging scans also indicate that in various convection-enhanced drug delivery protocols the interstitial fluid velocity decreases exponentially with the distance from the injection site (Sarntinoranont et al., 2006, Smith and García, 2009), with a decay rate which appears to depend on the type of tissue (i.e., white or gray matter). Our simulations indicate that high amounts of the drug can accumulate locally between the pipette tip and the cell and hence the effective concentration at the membrane level is consistently larger than the initial concentration in the pipette. The modelling results in terms of the delay between the beginning of acetylcholine application and the onset of the whole-cell current have been compared to a set of experimental data we obtained on TE671 cells. Some relevant predictions provide us with an estimate of the threshold level of nAChR activation required for the initiation of a measurable cell signal.

Section snippets

Physical Model

In a patch-clamp setup, the cell under study is placed in a bath solution which is relatively similar in composition to the extracellular environment. After reaching the desired recording configuration (whole-cell, in our case), the cell is positioned in front of the tip of the perfusion system, from where the activating drug (in the experiments presented here, acetylcholine) is applied. According to the standard pressure-controlled delivery method (Di Angelantonio and Nistri, 2001, Oancea et

General Equations

The experimental perfusion debit measured in our setup is Q ≈1 ml/(8 min) ≈1.938 μl/s. The corresponding flux of acetylcholine delivered through the pipette tip, which is assumed to be uniform over the entire perfusion surface, is then written as:Φ=Q×[ACh]p/Sp,0tτ0,t>τwhere [ACh]p represents the concentration of acetylcholine in the pipette solution, τ = 1 s is the duration of the pressure pulse, and Sp is the perfusion surface. In our simulations with various geometrical arrangements, we

Cell Cultures

TE671 cells of the human Caucasian rhabdomyosarcoma cell line (ECACC No. 89071904) were cultured in DMEM medium (Dulbecco's modified Eagle medium with GlutaMAXTMI and glucose 4.5 g/l, without sodium piruvate, GIBCO-Invitrogen), supplemented with 10% (v/v) fetal bovine serum, 50 units/ml penicillin and 50 μg/ml streptomycin. The cultures were grown at 37 °C in a humidified incubator with a 5% CO2 atmosphere. Subculturing was performed by trypsinization every 4-5 days, when the cultures reached

Diffusional Mass Transport

We first computed the maximal ACh concentration that builds up on the cell membrane as a result of simple diffusion (the convection term in Eq. (2) was set to zero) in a spherical domain. Fig. 4 presents the model results obtained with the two methods in the main geometry and conditions described in Section 3.2 (radius of the simulation domain: 1.5 cm) but with a different shape of the pipette tip (a truncated cone in the finite-element method, vs. the regular shape with four lateral flat faces

Discussion

We performed finite difference and finite element simulations of drug transport in a patch-clamp setup where the agonist (acetylcholine) is delivered by pressure application though a fine tipped pipette to an individual cell placed 500 μm away from the pipette. Our results indicate that with a release source distributed over a region of 600 μm in diameter and a pressure pulse duration of 1 s, the concentration of the drug reaching the cell depends not only on the initial concentration in the

Acknowledgements

This work was partially supported by the Romanian Ministry of Education and Research under CNCSIS-UEFISCSU Grant PNII-IDEI no. 1138/2009, code 1449/2008, and Grant PNII-IDEI no. 326/2007, code 251/2007. The finite element simulations have been performed at the Department of Bioengineering and Biotechnology of the Politehnica University Bucharest. We would like to thank Prof. Alexandru Morega for access to the laboratory and for his precious support and advice in the preparation of this paper.

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