Article pubs.acs.org/JPCB
Toward a Minimal Artificial Axon Amila Ariyaratne and Giovanni Zocchi* Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, United States ABSTRACT: The electrophysiology of action potentials is usually studied in neurons, through relatively demanding experiments which are difficult to scale up to a defined network. Here we pursue instead the minimal artificial system based on the essential biological componentsion channels and lipid bilayerswhere action potentials can be generated, propagated, and eventually networked. The fundamental unit is the classic supported bilayer: a planar bilayer patch with embedded ion channels in a fluidic environment where an ionic gradient is imposed across the bilayer. Two such units electrically connected form the basic building block for a network. The system is minimal in that we demonstrate that one kind of ion channel and correspondingly a gradient of only one ionic species is sufficient to generate an excitable system which shows amplification and threshold behavior.
1. INTRODUCTION
Similar simplified systems of a membrane with ion channels have of course been studied before from different perspectives and asked different questions. For example, Salman et al.1,2 working with patch clamped Xenopus oocyte membranes where a potassium channel was overexpressed were interested in the characteristics of the voltage noise supported by a collection of channels. Aimon et al.3 reconstituted and functionally characterized a voltage gated potassium channel in giant unilamellar vesicles, for the purpose of studying channel dynamics under precisely controlled membrane conditions. Two crucial (for our purposes) technical differences distinguish the present setup from these previous studies: a geometry which allows to interconnect more than one membrane patch, and a method that generates a useful voltage output signal from a voltage input signal, as it is necessary to implement a network. This has not been done before in a system with only one channel species, and also it cannot be done using the traditional approach of either the voltage clamp or the current clamp. With the former, one transforms a voltage input into a current output, with the latter the opposite. Our first attempt at an artificial axon geometry was a long, narrow supported bilayer strip separating two flow chambers; however, this setup proved to be too fragile. We therefore replaced the bilayer strip with a row of separate circular bilayer patches stretched across a corresponding row of holes in a solid state membrane, the bilayer patches being interconnected through flow chambers on either side of the solid membrane. The “unit cell” of this construction is two interconnected membrane patches, which is the system presented here. While a single supported bilayer patch is the traditional system for in
Neurons support efficient electrical signal propagation in water. The mechanism, while understood, is still fascinating from a physics perspectiveelectronics do not work very well under water. Signal propagation along the axon (or, more aptly, “signal regeneration”) is based on two fundamental processes: (1) ion pumps maintaining a concentration jump across the cell membrane for two different cations (Na+ and K+), and (2) voltage gated ion channels which, depending on the voltage across the membrane, open or close ion selective (either Na+ or K+) pores in the membrane. There is actually a third process which, while seemingly an imperfection, is absolutely essential for the working of the system, and that is small “leak” currents of Na+ and K+, even when the corresponding channels are “closed”. This situation allows for a steady state, nonequilibrium solution which supports signal propagation and conditioning. With respect to the above processes, the rest of the cell machinerymetabolism, gene expressionforms a background which keeps the cell alive but is otherwise separate (at least for time scales which are not too long). Therefore, from a synthetic biology perspective, rather than attempting to construct whole artificial nerve cells and networks thereof, it seems interesting to focus on artificial axons and their networks, which are more feasible. An artificial axon constructed from a user defined, simplified combination of cellular components (specific ion channels, specific lipids) could be very useful as an electrophysiology breadboard. In general, one goal is to eventually transfer to artificial axons at least a fraction of the electrophysiology research currently done on neurons, which come from lab animals. In this spirit, here we report on a minimal artificial system of lipid bilayers and ion channels where signal regeneration of the Hodgkin−Huxley type can be studied. © XXXX American Chemical Society
Special Issue: William M. Gelbart Festschrift Received: March 11, 2016 Revised: April 4, 2016
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DOI: 10.1021/acs.jpcb.6b02578 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B
V ≥ 0 mV and are “slow”. In the following, we refer to the physical mechanism of excitability outlined above as the “Hodgkin−Huxley mechanism”. To reiterate, in this paper the term “Hodgkin−Huxley mechanism” refers in a general way to an excitable medium consisting of a membrane with voltage gated channels, where the driving force for excitability comes from an imposed concentration gradient of the relevant ions across the membrane. By “excitability” we mean, more generally, the combination of threshold behavior and nonlinear amplification. The starting point for our artificial axon is a phospholipid bilayer patch stretched across a ∼ 100 μm circular aperture in a plastic support,7 separating the “intracellular” or “in” and “out” chambers (Figure 1). The “out” space is grounded; for the “in”
vitro studies of ion channel dynamics, we do not find previous studies of Hodgkin−Huxley signal propagation in this setting. In order to distill the truly minimal system, we make two further simplifications: (a) there are no ion pumps; instead, the concentration gradient of cations across the membrane is imposed externally; and (b) there is only one cationic species (K+) and corresponding ion channel. We demonstrate that in this system one can still propagate a voltage spike corresponding, loosely speaking, to half of the action potential. Before describing our results, we briefly summarize the relevant aspects of the Hodgkin−Huxley mechanism (see for example, ref 4). Consider a semipermeable membrane separating two water compartments (“in” and “out”) with different concentrations of cations (electrostatic neutrality being restored by corresponding concentrations of Cl− counterions, to which the membrane is completely impermeable). If there was only one cationic species, say K+, the membrane potential would hold steady at its equilibrium value (the Nernst potential), given by VNK = −
+ T ⎛ [K ]in ⎞ ln⎜ + ⎟ |e| ⎝ [K ]out ⎠
(1)
where V = ϕin − ϕout is the membrane potential, ϕ the electrostatic potential, e the electronic charge, T the temperature multiplied by Boltzmann’s constant, and [] indicates concentration. Eq 1 expresses the equality of the chemical potential μ of the ions inside and outside the cell, by using the dilute solution expression μ = μ0 + T ln[K+] + |e|ϕ
Figure 1. Two-well experimental setup which supports Hodgkin− Huxley signal propagation. Each well contains a bilayer patch stretched across a ∼100 μm hole (indicated by the 3 dots at the bottom of the wells); the ion channels are introduced by vesicle fusion to the bilayer. On the “extracellular” side, the wells are connected through the electrolyte solution; on the “intracellular” side, through an RC circuit. The extracellular side forms a common ground; the RC circuit on the intracellular side takes the place of a “synapse”, if we think of the two wells as two different excitable “cells”, or else it represents the passive, cable-like properties of the axon, if we think of the two wells as two different spots along the same axon. Each well is equipped with 3 AgCl electrodes: a voltage clamp (Vc), a measuring electrode (Ve), and a connecting electrode. The voltage clamp can be floated by toggling the relay switch S1. The current in the voltage clamp can be limited by opening the switch S2. The left well can be isolated from the right well by opening the switch S3. We change ionic concentrations in the experiment by carefully pipetting solutions in and out of the wells.
(2)
Notice that in order to establish this equilibrium, a small leak conductance for K+ ions across the membrane is essential. Similarly, if Na+ was the only cationic species, the membrane potential would hold steady at the corresponding Nernst potential for that species, VNa N . The voltage scale T/|e| ≃ 25 mV at room temperature while the concentration gradients maintained by the ion pumps in the living cell are such that, roughly, [K+]in/[K+]out ≃ 10 while [Na+]in/[Na+]out ≃ 1/10. The corresponding Nernst potentials are therefore VKN ≃ +60 mV and VNa N ≃ −60 mV, but the nonequilibrium steady state solution is a membrane potential (the resting potential) Vr =
χNa VNNa + χK VNK χNa + χK
(3)
space we have a voltage clamp and a separate high impedance voltage measurement; all electrodes are AgCl. The minimal axon consists of two such systems electrically connected. As a further simplification, we use an RC circuit for the “intracellular” connection (Figure 1), instead of an electrolyte bridge. In order to generate usable voltage signals, some thought must be given to the use of the voltage clamp. There are two alternatives: one is to “float” the voltage clamp at t = 0; this will generate a signal for t > 0. The other is to limit the current in the clamp to a value higher than the leak current with closed channels but lower than the ionic current with open channels. Specifically, if the clamp current is limited through a large resistance, Rc = 1/χc, the effect of the clamp is analogous to the effect of the Na+ term in eq 3, giving a resting potential:
in between these two values. Here, χNa, χK are leak conductances for the corresponding ions. Eq 3 expresses a steady state in which the total ionic current across the membrane is zero (the cell does not get charged over time). The steady state solution eq 3 is key to the propagation and regeneration of electrical signals in nerve cells: the resting potential Vr is neither equal to the equilibrium (Nernst) potential for the sodium ions nor for the potassium ions; opening of the Na channels drives the membrane potential to K VNa N (χNa ≫ χK in eq 3), while if the K channels open, Vr →VN. If the channels are voltage sensitive, there is the possibility of instabilities and signal amplification. The “signal” is either V = VKN or V = VNa N (V = Vr is no signal), so this system is inherently digital. A real action potential has a time course4,5 determined by further specific chracteristics of the voltage gated channels:6 Na channels open for V ≥ 10 mV, are “fast”, and are inactivate fast (close again independent of voltage); K channels open for
Vr = B
χc Vc + χK VNK χc + χK
(4) DOI: 10.1021/acs.jpcb.6b02578 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B
rapid vortexing for 30 min, resulting in a final lipid concentration of 20 mg/mL. This lipid solution was then sonicated for 20−30 min: the resulting unilamellar vesicles were stabilized in 10 mM DM for 30 min. Next, the concentrated ion channels solution was added to the vesicles solution, keeping a lipid to protein ratio of 1 (w/w). The concentration of detergent was then increased to 17.5 mM and the mixture incubated for 2 h with gentle vortexing every 20 min. The next step in the reconstitution is removal of the DM. The vesicleschannels mixture is passed 3 times through spin desalting columns (Pierce). Detergent absorbing bio beads (Bio-Rad) were then added to the mixture in adequate amounts. Every 12 h the bio beads were exchanged for new ones for a total of 4 cycles, with the sample kept at 4 °C. Prior to use, the bio beads were washed first in methanol, then in deionized water, and finally in reconstitution buffer. After the fourth cycle, the detergent free reconstituted channels were flash frozen in small aliquots (using an ethanol-dry ice bath) and stored at −80 °C for later use. The planar lipid bilayer is stretched across a hole in a plastic cup. We use the melt-and-shave method described in ref 7 to make a cone shaped indentation in a plastic tube (Ultra-Clear, Beckman Coulter). Shaving the tube with a sharp blade, one obtains a circular aperture of approximately 100 μm diameter. This support, or “well”, is then fixed to a Teflon holder that serves as the “extracellular” chamber. For each experimental run, fresh lipids from the −80 °C freezer are used; the lipids are dried as described above, then n-decane is added for a final lipid concentration of 20 mg/mL. A small drop ( 0. To reiterate: we want to use the voltage clamp to keep the system out of equilibrium (away from the Nernst potential), and also, we want to use a voltage signal to generate a voltage response from the artificial axon (for the purpose of eventually building a network). What is needed is neither a pure voltage clamp nor a pure current clamp, but something in between: a current limited voltage clamp. The ion channels (K+ channels, voltage gated, from Aeropyrum pernix: KvAP8−10) are expressed in E. coli and reconstituted in lipid vesicles. One or more vesicles are fused to the supported bilayer resulting in a membrane studded with oriented channels.11 We can achieve channel densities in the range 1−104 channels/(100 μm)2; the number of channels in the membrane patch is obtained from measurements of the ionic current. Ionic gradients are maintained typically as follows: [KCl]out ≃ 150 mM and [KCl]in ≃ 30 mM, giving a Nernst potential VN ≃ +40 mV. This pattern is reversed compared to real axons, but it allows, in our case, for signal propagation with only one type of channel. We hold the system at a “resting potential” Vr ≠VN using the voltage clamp.
2. METHODS The ion channel used for the experiments is the KvAP, a voltage gated potassium channel. The lipid bilayers are made with DPPC, a zwitterionic phospholipid. 2.1. Expression and Purification of KvAP Protein. The channel is expressed in E. coli cells (Stratagene XL1-Blue) using the expression vector pQE60. To transform the plasmid into the cells, we used a 45 s long heat pulse at 42 °C. All of the procedures below were performed at room temperature, and were adapted from ref 12. The protein expressed in E. coli (typically 10 g) was resuspended in 50 mL of lysis buffer (50 mM Tris at pH 8.0, 100 mM KCl, lysozyme 0.2 mg/mL, DNase 2 μg/mL, β-ME (2-mercaptoethanol) 2 mM, and protease inhibitor cocktail) and lysed by a French Press. The channels were extracted from the lysate in 40 mM detergent (Decylmaltoside: DM, Anatrace) for 3 h. The supernatant obtained by centrifuging the lysate-DM mixture was passed through a Talon affinity column (Clontech) to purify the Histagged ion channel using Cobalt beads. Before adding the protein supernatant, the beads were rinsed with 30 mL of wash buffer (20 mM Tris at pH 8.0, KCl 100 mM, imidazole 10 mM, and DM 5 mM). The mixture of beads and supernatant was rotated gently for 1 h and then passed through the column 4 times to retain all the beads in the column. Nonspecifically bound species were removed from the beads by rinsing with 30 mL of wash buffer, then the ion channels were eluted in 10 mL of elution buffer (which is wash buffer containing 400 mM imidazole). The His-tag was cleaved overnight in 1.5 units of thrombin (Sigma) for each milligram of channel protein. Removal of the thrombin was performed in a size exclusion Superdex-200 column (GE Healthcare), in HPLC buffer (20 mM Tris at pH 7.5, 100 mM KCL, and 5 mM DM), and finally the channels were concentrated to 10 mg/mL. 2.2. Reconstitution of the Channels into Vesicles and Membrane Preparation. Phospholipid vesicles were formed from the lipid DPPC (Avanti) through a procedure adapted from ref 13. The lipid was dissolved in chloroform and was dried under pure nitrogen flow, followed by adding ∼250 μL of pentene and drying. The dried lipid was then put under a vacuum for 1 h before being dissolved in reconstitution buffer (HEPES-KOH 10 mM at pH 7.4 with KCl 450 mM) through C
DOI: 10.1021/acs.jpcb.6b02578 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B
Figure 2. Detailed electrical connections for the one-well experimental setup. The electrode Vc is used for the voltage clamp, the electrode Ve is used to measure the actual membrane potential. The relay switch S1 is used to float the clamp, and the switch S4 is used to apply a load to the well (capacitance CL = 60 pF, resistance RL = 10 KΩ). If we think of one well as representing a small part of an axon, the RC load represents the rest of the axon. The membrane potential Ve is measured from the output signal of the op amp A2 (Ve = R1/(R1 + R2) Vout).
Figure 3. Picture of the experimental setup. The Teflon block mounted on the inverted microscope contains the “wells” (the circular holes give access to the top of the wells) and “extracellular chamber”. The system was designed for 3 wells, but only two are connected. The printed board next to the wells contains the head stage amplifiers of the two voltage clamps; the rest of the circuitry is contained in the printed board to the left. The computer screen shows 4 traces: a current trace (from the voltage clamp) and a voltage trace (from the Ve electrode) for each of the two wells.
Two-well system. Figure 1 shows the experimental setup of the two-well system. The setup consists of two plastic cups with small apertures (∼100 μm) in order to paint lipid bilayers. The two plastic cups are bathed in the same extracellular medium. Each plastic cup (referred to as a well) is connected to a head stage amplifier and a voltage amplifier. All electrical connections with the buffer were achieved with Ag/AgCl electrodes. Well 1 is connected to well 2 electrically as shown in Figure 1. This connection can be broken with the aid of the solid state relay S2. A 100 MΩ resistor was connected to the output of the head stage amplifier of well 1. A switch enabled the head stage amplifer to be connected to well 1 either with zero resistance or with 100 MΩ resistance. All electronics were connected to a data aquisition card (National Instruments PCIe-6323) and controlled/measured with a PC. In Figure 3 we show a picture of the setup. Initially both the intracellular chamber and the extracellular chamber are filled with the same buffer (150 mM KCl). Next a lipid bilayer was painted across the aperuture (or apertures in the two-well experiment) and the ion channels were incorparated to the lipid bilayer. After veryfying the activity of the ion channels, the buffer in the intracellular medium was slowly exchanged to a new buffer with lower potassium concentration.
Figure 4. Standard electrophysiology measurement of the channel current. The voltage clamp is held at −110 mV (channels closed), stepped up to +55 mV (channels open), then stepped back. The blue trace (Ve) shows the membrane potential recorded with the independent electrode Ve (Figure 2). The red trace (Ic) shows the current in the clamp. Here and for the next three figures, ionic conditions were [K+]out ≈ 150 mM and [K+]in ≈ 40 mM, giving a Nernst potential VN ≈ + 30 mV. The counterion was Cl− and the osmotic pressure was balanced with sucrose.
3. RESULTS We first characterize the one-well system Figure 2. One standard electrophysiology measurement is to clamp the voltage and measure the current, and this is shown in Figure 4. The voltage clamp is initially held at Vr = −110 mV (channels are closed at this voltage), then stepped to +55 mV (where channels are open with probability 1), and then returned to −110 mV. The blue trace (labeled Ve) shows the voltage in the intracellular chamber measured with the independent Ag/AgCl electrode. It follows the clamp voltage. The red trace (labeled Ic) shows the clamp current, sourced by the head stage amplifier. Initially, Vr = −110 mV and there is a corresponding leak current, quite large in this particular preparation (−1.5 nA in the figure). When the voltage clamp is stepped to +55 mV there is first a large capacitive current which charges the bilayer capacitance (in Figure 4 it is a spike in Ic masked by the trace of the voltage step); the channels open
with a characteristic time constant τ0 ≃ 25 ms and the ionic current peaks at a value Ip = Nχ(V − VN) reporting on the number of channels in the well, N. Here χ = 10 pA/60 mV is the single channel conductance, V the clamp voltage, and VN the Nernst potential corresponding to the ionic concentrations used. The subsequent decrease of Ic is due to channel inactivation, which for this system happens with a characteristic time scale of ∼400 ms.14 We have previously reported measurements of all these quantities in the one-well system.11 Here and in the following, the frequency cutoff of the electronics was ∼1 kHz while the intrinsic response time of the well system is much faster. However, in order to generate a voltage signal, we must proceed differently. Initially, the voltage is clamped at Vr = −120 mV (channels closed); then at t = 0 the voltage clamp is D
DOI: 10.1021/acs.jpcb.6b02578 J. Phys. Chem. B XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry B floated (the switch S1 in Figure 2 is opened). The voltage Ve measured at the independent electrode is shown in Figure 5.
100 channels (typical conditions in our present measurements) we find τ ≃ 10 ms, i.e., τ < τ0. Nonetheless, eq 8 does approximately reproduce the shape of the voltage front obtained by floating the clamp, as shown in Figure 6. The
Figure 5. Voltage signal (Ve) obtained by floating the clamp at t = 0. For t < 0, the clamp was held at −110 mV. The system “fires” up to the Nernst potential VN ≈ +35 mV. The voltage front has a characteristic shape in time seen in action potentials and approximately described by eq 8.
Figure 6. Voltage of the intracellular chamber (Ve) upon floating the clamp at time zero. For t < 0, the clamp was held at a “resting potential” of −110 mV. The gray trace is the experimental measurement, the red curve a fit with eq 8. The simulated trace was obtained by solving eq 8 with parameters that minimized the squared difference between the experimental trace and calculated trace. Those parameters were N0 χ/C = 100 s−1, qV0/T = −3.2, q/T = 0.15 mV−1, χl/χ = 1.2 × 10−2, and VN = 35 mV.
The process is that, because of the small but nonzero leak current, the voltage starts to rise when the clamp is floated, which drives more channels to open, raising the voltage further. Finally the voltage reaches VN. The voltage in Figure 5 has a characteristic shape also seen in the “first half” of an action potential in neurons. It comes about as follows. The steady state current through the membrane is I = Ic + Il = −N0pχ (V − VN) − N0χl (V − VN)
reason is that (2) the leak current associated with the leak conductance χl is an essential component of the system and governs the response. Given the initial condition V = Vr = −120 mV at t = 0, at short times p(V) ≃ 0 (given that p(Vr) = 0) so eq 8 reduces to
(5)
The first term is the channel current, the second the (small) leak current present even when the channels are “closed”. V is the membrane potential, N0 the number of channels, χ the single channel conductance, χl a “leak conductance” (χl ≪ χ), and p = p(V) the steady state probability that a channel is open, which approximately has the form: 1 p(V ) = −q(V − V )/ T 0 (6) e +1
N0χl dV =− [V (t ) − VN] dt C
(9)
governed by a characteristic time scale τl = C/(N0 χl) ≫ τ. Since for our system, χl/χ ≃ 1/100, we have τl ≃ 100 τ (l stands for “leak”). Figure 7 shows a control experiment in which there are no channels in the lipid bilayer (otherwise conditions are the same
Here q is a term proportional to the effective charge of the voltage sensor domian, and V0 is a term proportional to the energy difference between the open and closed states of the channel in zero applied voltage. The membrane patch is essentially a capacitance C which gets charged by this current:
dV =I (7) dt If we assume that the fraction of open channels follows in time its equilibrium value (eq 6), i.e., if opening and closing of the channels is “fast”, from eqs 5, 6, and 7 we have for V(t): C
χ⎫ N χ⎧ dV 1 = − 0 ⎨ −q(V − V )/ T + l ⎬[V (t ) − VN] 0 dt C ⎩e χ⎭ +1
(8)
The voltage front shown in Figure 5 should correspond to the solution of eq 8 for t > 0 with initial conditions V(t = 0) = Vr (Vr = −120 mV for Figure 5). From eq 8 we see that (1) in this regime, the characteristic time scale associated with voltage signals is τ = C/(N0 χ), which is the RC time constant with open channels; we would expect eq 8 to be valid for τ ≫ τ0 where τ0 is the characteristic time for the channels to switch. For the KvAP under the conditions of the present experiments, χ ≃ 10 pA/60 mV and τ0 ≃ 25 ms; further, for our ∼100 μm size membrane patch, C ≃ 50 pF, so for an example with N0 =
Figure 7. Control experiment with no channels in the bilayer. First the voltage clamp is stepped to +50 mV and back (to be compared with Figure 4), then (at t ≈ 5.2 s) it is floated (to be compared with Figure 5). Apart from capacitive spikes, the clamp current (black trace) stays at zero (
