Action potential modeling
Modeling of Action Potential Generation in NG108-15 cells Peter Molnar* and James J. Hickman NanoScience Technology Center University of Central Florida 12424 Research Parkway, Suite 400 Orlando, FL 32826 * Corresponding author Email:
[email protected] Phone: (407) 625-5700
Abstract In order to explore the possibility of identifying toxins based on their effect on the shape of action potentials, we created a computer model of the action potential generation in NG108-15 cells (a neuroblastoma/glyoma hybrid cell line). To generate the experimental data for model validation, voltage dependent sodium, potassium and highthreshold calcium currents as well as action potentials were recorded from NG108-15 cells with conventional whole-cell patch-clamp methods. Based on the classic HodgkinHuxley formalism and the linear thermodynamic description of the rate constants, ionchannel parameters were estimated using an automatic fitting method. Utilizing the established parameters, action potentials were generated using the Hodgkin-Huxley formalism and were fitted to the recorded action potentials. To demonstrate the applicability of the method for toxin detection and discrimination, the effect of tetrodotoxin (a sodium channel blocker) and tefluthrin (a pyrethroid that is a sodium channel opener) were studied. The two toxins affected the shape of the action potentials differently and their respective effects were identified based on the predicted changes in the fitted parameters.
Keywords Action potential, computer modeling, Hodgkin-Huxley, Linear thermodynamic description, drug detection, NG108-15, parameter fitting
Running Title: Action potential modeling
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Action potential modeling
1. Introduction Action potential generation and the shape of the action potential depends on the status of several ion channels located in a cell’s membrane, which are regulated by receptors and intracellular messenger systems {Gross, 1997 #139}{Gross, 1995 #138}{Morefield, 2000 #164}. Changes in the extracellular or intracellular environment (receptor activation, gene expression) can be reflected in an alteration of spontaneous firing properties such as the frequency and firing pattern {Xia, 2003 #215}{Amigo, 2003 #96}{Chiappalone, 2003 #7177}{Gross, 1997 #139} of excitable cells and in the changes of the action potential shape {Clark, 1993 #98; Muraki, 1994 #95; Nygren, 1998 #88; Akay, 1998 #85; Djouhri, 1999 #81}. Experimental data driven computer modeling has been an excellent tool to integrate our knowledge concerning elements of a complex biological system as well as to draw conclusions about the behavior of the complex system under different experimental conditions. These predictions can be correlated again with thenexperimental data. One typical example is the modeling of the electrophysiological behavior of an excitable cell. We have detailed knowledge about individual ion channels, as well as extensive knowledge about the behavior of the whole cell; but, we know relatively little about the interaction and modulation of ionic currents that shape the action potentials. One of the most complex single cell model created simulates the electrophysiological behavior of human cardiac myocytes {Nygren, 1998 #172; Nygren, 2001 #173}{Bernus, 2002 #100}. This model was validated based on electrophysiological experiments in physiological and pathophysiological conditions {Winslow, 2001 #8717} and used for deeper understanding of behavior of ion channels in diseases. The most commonly used mathematical formalism which describes the action potential generation in excitable cells was developed by Hodgkin and Huxley in 1952 {Hodgkin, 1952 #7255}. In our studies we have used this formalism, although for the description of the ion channels we utilized the linear thermodynamic approach, which, in our opinion, was more general and does not require ‘guessing’ the form of the functions describing the voltage dependence of the state parameters {Destexhe, 2000 #115}{Weiss, 1996 #12305}. We used the NG108-15 neuroblastoma/glioma cell line in our studies {Mohan, 2006 #12307}, because these cells do not form synapses in culture, thus they are ideal single cell sensors {Kowtha, 1993 #3614}{Ma, 1998 #7211}.
2. Materials 2.1. NG108-15 cultures 1. Culture medium: 90% Dulbecco’s modified Eagle’s medium (DMEM, Invitrogen) supplemented with 10% Fetal Bovine Serum (Invitrogen) and 1% HAT supplement (Invitrogen) 2. Differentiating medium: DMEM + 2% B27 supplemet (Invitrogen) 3. Poly-D-Lysine (PDL) solution: 5 mg PDL (Sigma, P7405) in 500 ml water, sterile filtered
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Action potential modeling
2.2. Patch-clamp recording of ionic currents and action potentials 1. Extracellular solution: 140 mM NaCl, 3.5 mM KCl, 2 mM MgCl2, 2 mM CaCl2, 10 mM Glucose, 10 mM HEPES, pH = 7.34 2. Extracellular solution for the recording of potassium currents: Extracellular solution + 1 µM Tetrodotoxin (Alomone Labs, T550) 3. Extracellular solution for the recording of sodium currents: 50 mM NaCl, 100 mM TEA-Cl, 5 mM CsCl, 1 mM CaCl2, 1 mM CoCl2, 1 mM MgCl2, 10 mM Glucose, 10 mM HEPES, pH = 7.34 4. Extracellular solution for the recording of calcium currents: 100 mM NaCl, 30 mM TEA-Cl, 10 mM CaCl2, 2 mM MgCl2, 10 mM Glucose, 10 mM HEPES, 1 µM Tetrodotoxin, pH = 7.34 5. Intracellular solution for action potential and potassium channel measurement: 130 mM Kgluconate, 2 mM MgCl2, 1 mM EGTA, 15 mM HEPES, 5 mM ATP, pH = 7.2, osmolarity = 276 mOsm 6. Intracellular solution for sodium channel measurement: 130 mM CsF, 10 mM NaCl, 10 mM TEA-Cl, 2 mM MgCl2, 1 mM EGTA, 10 mM HEPES, 5 mM ATP 7. Intracellular solution for calcium channel measurement: 120 mM CsCl, 20 mM TEA-Cl, 2 mM MgCl2, 1 mM EGTA, 10 mM HEPES, 5 mM ATP. For selecting L-type calcium channels, 1 µM ωCTxGVIA (Tocris) was added 8. Pipette puller (Sutter, P97) 9. Glass pipettes (Sutter, BF150-86-10) 10. Vibration isolation table with Faraday cage (TMC, Peabody, MA) 11. Microscope Axioskop 2 FS plus (Zeiss) 12. Patch clamp amplifier Multiclamp 700A (Axon), A/D converter Digidata 1322A (Axon), patch clamp software pClamp 8 (Axon)
2.3. Obtaining the parameters describing ion channel currents and action potentials in NG108-15 cells 1. Matlab software (MathWorks)
2.4. Effect of drugs on action potential shape and on ion channel parameters 1. TTX (Alomone Lab) 2. Tefluthrin (Riedel-de Haën)
3. Methods 3.1. NG108-15 cultures 1. The NG108-15 cell line (passage number 16) was obtained from Dr. M. W. Nirenberg (NIH). Cells were stored frozen in liquid N2 in 1 ml vials (1 million cells/vials) 2. Cell stock was grown in a T-75 flask in culture medium at 37°C with 10% CO2 (Notes 1). 3. Glass coverlips were cleaned by concentrated nitric acid for 30 min, rinsed 3 times with water and sterilized by submerging in 100% alcohol for 20 min.
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Action potential modeling 4. Coverlips were placed in 6-well plates and were incubated in poly-D-lysine solution for 1 h in the 37°C incubator. 5. After confluence, the culture medium was replaced by 6 ml differentiating medium. The cell layer was dislodged by knocking the flask to the table. Cells were dissociated by tituration in a 5 ml pipette. 6. NG108-15 cells was plated in a density of 40,000 cells / 35 mm culture dish in 2 ml differentiating medium on the PDL-coated coverslips and were cultured for one week at 37°C with 5% CO2
3.2. Patch-clamp recording of ionic currents and action potentials 1. Coverslips were transferred into a chamber on the microscope stage, which was continuously perfused with the appropriate extracellular solution. Experiments were performed at room temperature. 2. Glass pipettes, pulled with the electrode puller, were filled with the appropriate intracellular solution and had a resistance of 4-6 MOhm 3. Signals were filtered at 2 kHz and digitized at 20 kHz 4. Sodium and potassium currents were measured in voltage clamp mode using 10 mV voltage steps from a –85 mV holding potential. To record high-threshold calcium currents, a – 40 mV holding was used. 5. Whole cell capacitance and series resistance was compensated and a p/6 protocol was used. 6. Action potentials were evoked with short (2 ms) current injections in current clamp mode either at resting membrane potential or at a –85 mV holding potential. Data was saved in text-format and imported into MATLAB for further analysis. 7. Tip potential was calculated by the built-in routine of the pClamp program and was compensated by subtracting 15 mV from the membrane potential values.
3.3. Obtaining the parameters describing ion channel currents in NG108-15 cells 1. A computer program was created in MATLAB to fit parameters to the recorded data according to the following equations. Basically, the experimental data was given as total ionic current vs. time (note, that sodium, potassium and calcium currents were measured independently in separate experiments) and membrane potential vs. time. 2. Total ionic current (sodium INa, potassium IK calcium ICa and leakage channels Il included): I ionic = I Na + I K + I Ca + I l = g Nam3h(V − VNa ) + g K n4 (V − VK ) + g CaLe3 (V − VCaL) + g l (V − Vl ) Where g Na , g K , g CaL , VNa , VK , VCaL are parameters (maximum conductances of the channels and reversal potentials, respectively) and m, n, h, e are the state variables 3. The dynamics of the state variables: dm m∞ − m = Where m∞ , n∞ , h∞ , e∞ are the steady-state values of the state τm dt variables and the τ -s are their voltage-dependent time-constants.
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Action potential modeling 4. The voltage dependence of the time constants and the steady-state state parameters were given according to the general thermodynamic formalism. Example was given for the m state parameter: 1 m∞ = and zF − (Vm −V 1 ) 2 RT 1 + exp
A
τm = exp
zF ξ (Vm −V 1 ) 2 RT
cosh(
zF (Vm − V 1 )) 2 2 RT
Where z, V 1 , A and ξ are fitting parameters and Vm represents the membrane 2
potential. As it can be seen from these equations V 1 corresponds to the half 2
5.
6. 7. 8.
activation/inactivation potential of the channel and A is linearly related to the activation or inactivation time-constant. The meanings of z and ξ are not as obvious: z is related to the number of moving charges during the opening or closing of the channel; whereas ξ describes the asymmetric position of the moving charge in the cell membrane. Sodium, potassium and calcium channel mediated current data, which were recorded in voltage-clamp mode at different membrane potentials (5 mV increments, -40 mV, +30 mV range), were imported into MATLAB. Based on the above equations, simulated current traces were calculated (Figure 1). An error function was generated based on the difference between the recorded and the simulated traces through the whole voltage range (Note 2 and 3). Matlab’s fminsearch routine was used to optimize the parameters to minimize the error function (Note 4) Parameters obtained from different cells were averaged (n = 4-6) and considered as initial values for the action potential modeling
3.4. Fitting parameters to the experimentally recorded action potentials 1. Effect of the currents on the membrane potential: dV I external − I ionic = dt CM Where Iexternal is the externally injected current used to depolarize the membrane and evoke the action potential in current clamp mode. 2. The following parameters were obtained from the patch-clamp recordings and used in the modeling: membrane resistance, resting membrane potential, membrane capacitance and injected current. The maximum conductance of the leakage current (gl) was calculated from the ionic conductances and from the resting membrane potential.
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Action potential modeling 3. The differential equation above and the differential equations for the state parameters are forming a first order coupled differential equation system, which was solved with Matlab’s ODE23 solver. 4. Parameters determining the simulated curve were fitted to the experimental data using the fminunc routine.
3.5. Effect of drugs on action potential shape and on ion channel parameters 1. Drugs were applied by perfusing the experimental chamber with the drug containing extracellular medium 2. Action potentials were recorded before and 10 minutes after the drug administration 3. Ion channel parameters were calculated for the control and for the drug modified action potentials by fitting the simulated action potentials to the recorded experimental data (Figure 2, Table 1) 4. Drug effect was quantified as percentage changes in the ion channel parameters obtained before and after drug administration.
4. Notes 1. Cells grew well at 5% CO2 2. Curves were fitted after an initial 0.1 ms delay to eliminate the effect of experimental artifacts 3. To quantify the difference between the fitted curves and the recorded data the following error-functions were implemented: Maximum error: E Max = Max ( Abs( R(t n ) − S (t n ))) where R(tn) is the recorded value and S(tn) is the simulated data at time tn. Least Square: E Lsquare = ∑n ( R(t n ) − S (t n )) 2 . Weighted Least Square: EWLsquare = ELsquare if tn
