Microsoft Word - Libro CompletoEFFECT OF TWO PORE DOMAIN POTASSIUM CHANNEL
A thesis submitted for the degree in Physics at Universidad de Los Andes Experimental work carried out in
Biophysics Section Blackett Laboratory
by
Co-Assessor
January 2006
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ABSTRACT The aim of this Project is to do a research in the nerve system of the Lymnaea Stagnalis specifically the study of the 2-Pore domain potassium channel in order to find its mammalian counterpart. To be able to make a comparison between the snail’s channel and the human one, it was necessary to applied the concepts given in an article published in 2004 by Marco Gruss and his group titled “the two pore domain K+ channels TREK-1 and TASK-3 are differentially modulated by copper and zinc”. By following the above method we started modulating the lymnaea’s channel by making two separate solutions, one of copper and another one of zinc. We wanted to see if the behaviour of the channel in the Lymnaea had the same features as in the human ones explained in the article. For example: If the lymnaea’s channel was TREK-1 we were expecting to see an inhibition when a high concentration of zinc (i.e. 200uM) was used, and to see an activation with a low concentration of copper (i.e. 10uM). However, if the channel was TASK-3, it should inhibit with low concentrations of zinc (20uM) and copper (5uM). It is important to understand that these two metals were combined with 8% of halothane to be able to get the best activation of the channel.
Besides the application of physics, this Project involves the use of two more sciences such as: Neurology which is applied at the beginning of the procedure, by dissecting the snail to be able to obtain the right parietal ganglion. This ganglion contents the nerve system of the snail which is made of four cells, and three of them have the channel to be studied (2-pore domain potassium channel). Electrophysiology is applied in order to obtain the neuron of the snail by measuring its electrical behaviour.
Initially, we intended to isolate one of the neurons out of the ganglion to avoid the nearest neurons affecting the final results. However, this was only achieved once, since we discovered it was taking us too long and it was too risky. So, we decided to leave it attached to the ganglion, but kept in mind that the time used to exposed the neuron to the solution had to be longer to be able to keep the ganglion in an equilibrium. All of this is done in order to obtain the best and more precise results.
The method used in our investigation is called The Voltage Clamp, which consists in impelling the cell by using two electrodes to measure the potassium current keeping the same voltage of the cell. In this way, we can have a plot of voltage against time and at the same time a plot of current against time, but they can be unified to obtain a plot of voltage against current.
Once the neuron has been impelled the next step is to bathe it with a control solution (GSR), which is known for having the same characteristics of the substance found in the brain of the snail, allowing the neuron to be alive and healthy during the whole process. Therefore, the current in steady stated can be measured. Then, the ionic current affected by halothane is measured, expecting a big activation of the channel. If this happens, we can say that we are in the
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right cell, otherwise it will be necessary to look for another one or in the worse scenario will have to start all over again. Now, if we are in the correct cell we have to measure the effect in the current given by any of the two test solutions (Halothane plus zinc or halothane plus copper). After this, it is necessary to repeat the same process one more time, but this time we do not include the test solutions in order to make sure that the effect of the anaesthetics and the metals can be completely reversible. Therefore, the results are determined by a temporary change in the gradient concentration due to the solutions, but if the change that occurs is permanent we could say that there is a weak cell. This way we have a plot containing all the different channel behaviours (Control, Halothane and Test solutions) and these plots have to intersect in the same point called reversal potential, which in this case is the same potassium resting potential. This procedure is repeated with different neurons and snails in order to obtain great confidence in the results and to help us get an average behaviour of the channel and this way it is possible to compare our results with the ones given by Gruss.
Therefore, the potassium channel resistance for a Lymnaea Stagnalis is represented based on the Ohm’s law. Taking into account that the result can be affected by different factors, the plot obtained does not have to be completely linear. So, the final result is a qualitative and not quantitative measure, which let us see when the channel is activated or inhibited by the solutions, allowing or not the flow of ions through the cell. By following all the previous procedures we found out that the Lymnaea potassium channel is neither TREK-1 nor TASK-2, leaving an open door for future investigations of the Lymnaea channel based on the characteristics of any channel member of the 4TM-2P potassium channel family found in humans.
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ACKNOWLEDGEMENTS
I would like to thank professor Nick Franks of Imperial College for trusting me and giving me the opportunity to be part of his Biophysics group. Also for letting me work on my research with all the advantages and benefits a researcher can have. He and his wife Angie supported me unconditionally in every step of my project and they were always willing to help me when I had any personal problem or any other difficulty during my stay in London. Their friendship helped me to have the strength to be able to go through many different situations. I am grateful to Dr Robert Dickinson for his support during my whole project at Imperial College, for giving me advice when I needed it, and helping me to resolve problems at the lab which would not have allowing me to obtain the good results that I got. I know that I could never have achieved this without his encouragement, his friendship and his moral support that made me feel I was not alone. I would like to express my thanks to Mr Adrian Hawksworth for helping me to find the legal way that permitted me to be a student at Imperial College, and for giving me the right tools that help me to perform my research more efficiently. I also want to thank Raquel Yustos for taking care of my snails, for supplying all the materials that I needed and for helping me to learn a lot more about chemistry and biology. I could keep giving thanks to a lot of more people who helped me in every aspect of my life in London, but I hope to be able to do it by expressing my thanks to the entire Biophysics group of Imperial College. They always cared about me, and they were always willing to help me in any situation, making my research one of the most wonderful things I have ever done in my life. I owed particular thanks to Dr Carlos Avila in Colombia, for his unconditional support, even though all the problems that I had he always trusted me and encourage me to finish my project with great success. He made possible for me to have this project accepted by Universidad de Los Andes. I would also like to thank Dr Chad Leidy for guiding me and helping me to finish this project. For his feedback and invaluable suggestions that made of this book a very valuable guide which can be used by any one interested in understanding or continuing working on this topic.
Above all, to Andres Roa for his unconditional love and trust and for being with me in good and bad times during many years, for supporting me and helping me to achieve all my goals. Last but not least important I am eternally grateful to my family for supporting me in all kinds of different ways. They were always there for me no matter what, for helping me to make all my dreams come true and for giving me the strength I needed each day to be able to achieve all my goals, no matter how hard and how far away they have been.
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CONTENTS
1.1 INTRODUCTION ......................................................................................................9 1.2 THE CELL MEMBRANE ........................................................................................10 1.2.1 RESTING POTENTIAL 12 1.2.2 ION TRANSPORT 12 1.2.3 ACTION POTENTIAL 13 1.2.4 NERVE IMPULSE 15 1.3 ION CHANNELS.....................................................................................................15 1.4 PHYSICAL CONTEXT............................................................................................19 1.4.1 THE MEMBRANE AS AN ELECTRIC CIRCUIT 20 1.4.2 THE NERNST EQUATION 22 1.4.3 THE GOLDMAN EQUATION 24 1.4.4 THE HODGKIN AND HUXLEY MODEL (HH) 26 1.5 ANAESTHESIA......................................................................................................33
2 CHAPTER 2 – MATERIALS AND METHODS ................ 38
2.1. AN INTRODUCTION TO VOLTAGE CLAMP TECHNIQUE...................................38 2.2. ELECTRODES .......................................................................................................39 2.3. PERFUSION SYSTEM ...........................................................................................41 2.4. PREPARATION OF THE NEURAL TISSUE ..........................................................43 2.4.1. DISSECTION 44 2.5. ELECTROPHYSIOLOGY.......................................................................................47 2.5.1. VOLTAGE TO FREQUENCY CONVERTER 48 2.6. DATA ACQUISITION .............................................................................................49 2.7. SOLUTIONS...........................................................................................................51
3.1. MAIN NEURONS CHARACTERISTICS.................................................................54 3.2. INVALID RESULTS AND DATA SELECTION.......................................................57 3.3 CHARACTERIZATION OF SNAIL TWO-PORE POTASSIUM CHANNEL, AND COMPARISON WITH HUMAN TASK-3 AND TREK-1 POTASSIUM CHANNELS........63 3.3.1. NO RESPONSE FOR LOW ZINC 63 3.3.2. HIGH ZINC RESPONSE SUGGESTS TREK-1 65 3.3.3. NO ACTIVATION BY COPPER 66 3.4. POSSIBLE STRATEGIES FOR IDENTIFYING THE SNAIL POTASSIUM CHANNEL.......................................................................................................................69
4 CONCLUSIONS.................................................................... 71
the voltage sensor [14]. .........................................................................................18 Fig. 1-10 Potassium channel with delayed rectifier and its domains.......................18 Fig. 1-11 Shows some families of (4TM-2P), and its unfolded structure [14]. .........19 Fig. 1-12 Shows polarization (A) and hiperpolarization (B) of neurons in the
Lymnaea Stagnalis with external currents of 1nA, generating the charge and the experimental discharge of the cellular membrane. ......................................21
Fig. 1-13 Shows the Hodking-Huxley model [7]. ........................................................28 Fig. 1-14: a) shows the potassium and sodium conductance in function of time. b)
I Vs E [7] ..................................................................................................................30 Fig. 1-15 Shows the τn and n∞ plots [7] ........................................................................32 Fig. 1-16 Hypothetic representation of polarization and hyperpolarization [7].......33 Fig. 1-17 Schematic drawing of four types of membrane associated drug targets
[6]. ............................................................................................................................35 Fig. 1-18 Halothane Chemical Structure [3]................................................................35 Fig. 1-19 Halothane hyperpolarize the spikes of action potential [3].......................36 Fig. 2-1 Circuit of 2-electrode voltage clamp technique............................................39 Fig. 2-2 a) Microelectrode Puller, b) Enlargement of microelectrode puller c)
Electrode holders. ..................................................................................................40 Fig. 2-3 Shows the Perfusion Table.............................................................................41 Fig. 2-4 a) Shows the perfusion system including valves V1 and V2, b) Shows the
V3 together with valves V1 and V2. ......................................................................42 Fig. 2-5 a) Electrophysiology table and b) Perfusion table showing the impel and
the full perfusion table including the glass used to suck the solution. ............43 Fig. 2-6 Tank used to keep the snails fed with Iceberg Lettuce ...............................43 Fig. 2-7 Shows the whole dissection procedure, until an isolated ganglion...........46 Fig. 2-8 Shows the way to obtain a ganglion holder, by pulling the pipette until the
necessary radius is obtain. The right side is connected to a long rubber tube, used to suck the ganglion. ....................................................................................46
Fig. 2-9 Shows the ganglion held by the thin pipette. ...............................................47 Fig. 2-10 Shows an isolated single neuron, hold by the two electrodes. ................47 Fig. 2-11 shows the neuron in the ganglion impelled by the two electrodes..........48 Fig. 2-12 A circuit for a voltage to frequency converter [11] ....................................49 Fig. 2-13 A circuit for a ten times amplifier operational [12].....................................49 Fig. 3-1 Diagram showing the nerve system enumerated.........................................54 Fig. 3-2 Three main features of a steady state in a current against voltage plot....55
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Fig. 3-3 Shows the steady-state current (cells are bathed with control solution) against voltage plot for each cell in the nerve system. ......................................56
Fig. 3-4 Potassium channel behaviour,.......................................................................57 Fig. 3-5 shows statistics to data collection. ...............................................................58 Fig. 3-6 shows a cell that can not be activated by halothane. ..................................58 Fig. 3-7 shows a current against time plot showing a usual noise shape...............59 Fig. 3-8 shows how the spike can be mixed up with noise.......................................60 Fig. 3-9 a) shows the action potential when the Axoclamp is in bridge mode. b)
shows the spikes normal behaviour at -30 mV in voltage clamp mode. ...........60 Fig. 3-10 shows a typical plot in which the resting potential for a cell is different in
each solution, showing the plots have different reversible potential. ..............61 Fig. 3-11 Typical plot in which the three plot cross the reversal potential,.............62 Fig. 3-12 The cell is bathed with control solution and the red plot is obtained. After
that, halothane is added (green) and finally the black plot shows an inhibition of the potassium channel by 8% Halothane plus zinc 20 uM. All the plot looks as a valid data, but they are not. ...........................................................................62
Fig. 3-13 show the plot for each zinc coyncentration and the potassium channel behaviour. ...............................................................................................................64
Fig. 3-14 Shows the behaviour of human TASK-3 affected by low zinc. ................65 Fig. 3-15 Shows and 14% inhibition by zinc 200 uM..................................................65 Fig. 3-16 the left side it is shown the human TREK-1 modulated by zinc and in the
right side is the behaviour of human TASK-3 affected by copper [3]. ..............66 Fig. 3-17 Copper results for human TREK-1 [3] .........................................................66 Fig. 3-18 shows the behaviour of the two different cells of Lymnaea affected by
copper 10uM. ..........................................................................................................67 Fig. 3-19 summary of concentrations of zinc, ............................................................68 Fig. 3-20 Gruss et al., 2003 datas for human TASK-3 and TREK-1 [4] .....................69 Fig. 3-21 Shows the behaviour for the different 2 pore domain potassium channel.
Showing a way to differentiate all of them [10]. ..................................................70
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1.1 INTRODUCTION
The human being is a collection of information. The main goal of a physicist is to find relations within this information in order to comprehend the unexplored mechanisms that govern the universe and the human body. We are never satisfied, and this curiosity is the pillar of our field. One of the most exciting and important subjects is the brain, due to its complexity and its essential role in animal behaviour. The most basic problem in understanding the brain is the study of ion channels in a single nerve cell. Ion channels{ XE "Ion channel" }{ XE "Ion channel" \b } are the main functional components in the neuron, and are responsible for the electrical signalling. Basic studies on ion channels are done in order to understand how neurons transfer the information across the brain and generate a behavioural response. In this chapter we pretend to provide background information about ion channels, and specifically about potassium channels{ XE "potassium channels" \b }{ XE "potassium channels" }, in order to study and investigate in the following chapters more specifically an aesthetic- activated potassium channel that is found in the pond snail Lymnaea stagnalis.
First of all, an understanding of how neural signalling functions is needed. We begin by presenting the basic structure of the neuron. As in other cells, the neuron is surrounded by a plasma membrane. In contrast with other cells they have unique structural elements such as; the axon, the dendrites and synaptic terminal, which are specific to their electrical networking. The axon is responsible for intracellular information transfer. The dendrites receive and integrate the information from other cells, working together with the axon in the electric signalling. Finally, the synaptic terminal is responsible for the intercellular transfer of information. This ability to transfer information between cells is the basis for the complex electrical activity of the brain. A neuron is shown in Fig. 1-1.
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Fig. 1-1 The Neuron Structure [17]
Another important characteristic of neurons is that these cells are enriched in proteins called ion channels, which as mentioned before are responsible for the electric signalling. Different types of ions (i.e. Na+, K+ and Ca-) are present in the intracellular and extracellular space of the neuron, and the ion channels regulate the difference in ion concentrations between the inside and the outside of the cell. Not all neurons have the same ion distributions. These variations differentiate the behaviour of different neural networks. The next sections pretend to clarify in more detail how ion flows across the membrane can generate the transport of information through the neurons. For this, it is necessary to clarify the importance of the membrane potential, the resting potential, ion flows, and the physical behaviour of neurons in general.
However, it is necessary to point out that the transmission of information through the neuron is not only controlled by the different ions flows that are induced. In addition, there are different mechanisms to manipulate the electric neural signals through chemical species that regulate the ability of neurons to transmit electrical signals. These regulatory mechanisms are useful for the experimenter. They are based in the use of anaesthetics, which are compounds that interact directly with ion channel and regulate their activity. For this project, a specific type of ion channel was chosen in Lymnaea Stagnalis, which is affected by specific anaesthetics. For this reason, it is important to also discuss the main features of anaesthetics and their role in regulating ion channels behaviour.
1.2 THE CELL MEMBRANE { XE "CELL MEMBRANE" \b }{ XE "CELL MEMBRANE" \b }{ XE "CELL MEMBRANE" }
An important characteristic of the cell membrane is that it is impermeable to many substances. Since the neural plasma membrane is composed by a double layer of phospholipids molecules about 4 nm in thickness it behaves as a barrier to polar species such as ions. These amphiphilic molecules are composed by a headgroup facing the water interface and a tailgroup facing in the mid-section of the membrane [1]. See Fig. 1.2
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The membrane contains protein channels that allow the passive penetration of specifics ions. At the same time, other ions are pumped actively across the membrane by specific ATP dependant channels. These pumps maintain a negative charge inside the neuron with regards to the outside, therefore inducing a voltage potential. Variations in the electric potential induced by the flow of ions across the membrane are the basis for the transport of information. These variations in the electric potential travel from the axon terminals in one neuron to the contact site with other neurons, where the intercellular signal is generated between neurons.
Since neural signalling is based on the presence of ion currents across the membrane, the neural membrane can be approximately modelled as an electric circuit. In this circuit, the lipid bilayer acts as a capacitor connected in parallel with a resistor which represents the ion channels. The capacitance is about 1µf/cm2 while the conductance depends on the intrinsic property of the ion channels. Hence, the specific ion channel conductance, the ionic concentration and the different types of ions give the total conductance of a cell. A circuit is shown in Fig. 1.3.
Fig. 1-2 Neuronal Membrane [7]
Fig. 1-3 Approximation of an electrical behaviour of a cell membrane [7]
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1.2.1 RESTING POTENTIAL
The resting distributions of ions across the membrane induce an electrochemical potential. This distribution (ion gradient) involves differences in the internal and external concentrations of Na+, Cl-, K+ and Ca+ ions resulting in a steady state voltage across the membrane. When the axon is not conducting nerve impulses, these ion distributions are in equilibrium with regard to their electrical and chemical potentials. The opening of specific channels takes the system out of equilibrium and induces an electrical impulse. This impulse is responsible for the electrical signalling in neurons.
The resting potential is usually between -40 and -90 mV, which results from the fact that inside of the cell has at least 20 times more K+ ions than the outside, while the outside of the membrane has at least 20 times more Na+ ions and 9 times more Cl- ions than the inside [1]. See Fig.1.4. This resting electrochemical potential is induced by differences in the transport of ions through activation of specific ion channels.
-100
-80
-60
-40
-20
0
Vo lta
ge (m
1.2.2 ION TRANSPORT
The transport of ions across the membrane can be active or passive. The active process requires the expenditure of energy while the passive process is the result of random diffusion of molecules. The different passive transport mechanisms employed are. Osmosis: The movement of water molecules form an area of high concentration to an area with low concentration. Carried mediated diffusion: Takes place when a molecule is bound to a carried molecule that moves quickly through the membrane an example could be the transport of glucose and amino acids across the cell membrane. The active transport mechanisms that use energy to pump ions against there concentration gradient, established and maintain the resting potential, see Fig. 1.5. A key pump is the Na-K pump that uses energy stored in ATP molecules to pump Na+ out of the cell
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and K+ in. On the other hand, there are different kinds of exchange pumps that use the energy inherent in the concentration gradient of one ion type in order to pump another ion type against concentration gradient. For example, Na-Ca exchanger removes Ca2 from the cell at the cost of Na entry. We will focus in the ionic current given by the pump Na-K [1]. Sodium potassium pump: Given that the charge gradient does not weaken with time setting a resting potential, presumes the existence of a Na-K pump, which sends three sodium ions for each two potassium ions that enter. On the other hand, the chlorine ions do not affect the interior potential set by the potassium and sodium ions [7]. Since the chlorine ions are free to cross the membrane by means of a passive process. (See Fig. 1.5.
Fig. 1-5 Sodium potassium pump [18]
1.2.3 ACTION POTENTIAL
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The flow of ions is regulated by chemical and electrical stimulation. The voltage across the membrane changes when a neuron is stimulated electrically. The membrane has been depolarized if the stimulation produces a change that decreases the resting voltage in the membrane. This is due to the movement of sodium ions into the cell. On the other hand, the membrane has been hyperpolarized if the stimulation produces a change that increases the voltage across the membrane. This is induced by an increase in potassium ions on the outside of the cell. This suggests that a chemical or electrical stimulation induces a change in the membrane channels that either decrease or increase the movement of ions across the membrane.
The propagating action potential is an electrical response of excitable cells Fig 1.6. The key properties of an action potential are the high conduction speed, briefness, and fast recovery. High speed usually needs high activation of Na+ channels. Briefness usually requires fast inactivation of Na+ channels and high K+ permeability. The high K+ permeability comes from fast activating delay rectifier K+ channels in the majority of excitable cells presenting short action potential (1 to 10 ms durations at 20°C).
Fig. 1-6 Action potential [19]
Fig 1.6 shows systematically the action potential in the neuron. The
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membrane is originally in its rest potential. The membrane is then usually affected by a short intense stimulation (approximately 0.5 milliseconds) and the voltage between the layers is depolarized down to -50 mV (1). At this point the membrane is completely permeable to the sodium ions. The flow of sodium ions induces a change in the voltage up to 0 mV, even reaching up to +50 mV. Then the membrane becomes completely permeable to the potassium ions (2), which block the flow of sodium ions (3), and restore the voltage back to its resting state (4). The flow of potassium ions can even induce the voltage to exceed the resting potential (5). When this happens, the membrane recovers its state of rest under the action of the Na-K pump, recuperating potassium ions that were left outside (6) [19].
1.2.4 NERVE IMPULSE Through the use of propagating action potentials the information through the organisms is transported. The action potential propagates in the extreme axon at a speed of 1 to 100 meters per second. A key feature of the nerve impulse is that once the impulse is set off, it needs no further stimulation to keep propagating. The neuron provides the necessary energy to maintain the nerve impulses propagating, which are all identical in magnitude. Based on this, action potential presenting intermediate situations are not expected. Differences in resistance to the current through the axon cause the nerve impulses not to travel at the same speed in all the neurons, since the speed of the impulse decreases when the resistance increases. By knowing the variation in resistance for different neurons the transport of ions across the membrane is fully describe throughout the organism.
1.3 ION CHANNELS
Now, that the characteristics of electrical signalling have been explained, it is important to understand in more detail, the types of ion channels that can exist in neurons as well as their properties. In this way a general classification of the ionic channels will be given, but emphasising the ion channel studied in this project (the 2-pore domain potassium channel). Proteins genetically encoded form ion channels, also called pores. They are highly selective filters that allow only specific ions to diffuse through the cell membrane. The ion channels are denominated gated if they can be opened or closed. There are three different types of gated ion channels: mechanically gated, voltage gated and ligand gated. We present a brief description of these three and their relationships with simple diffusion, facilitated diffusion and active transport [1].
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Fig. 1-7 Cone ionic structure [15].
Fig 1.7 shows its structure made of specific aminoacids that provides the
channel with the ability to select a specific type of ion, since the channel recognized and filtered the ion into the intracellular zone, based on the structural geometry of the pore and the valency of the ion. The voltage sensor is a transmembrane region also called domain that recognized the voltage difference necessary to open and close the pore at a certain moment of the action potential.
Ligand gated channels: A small signalling molecule or ligand opens or closes the channels in response to binding. Some ion channels are gated by extracellular ligands, others by intracellular ligands. Ligands are molecules that interact with these types of channels, producing a structural change in the protein, which induces the ionic channel to open. Therefore, the ligand is an agonist particle that can activate or inhibit the ionic channel (see sec 1.5). For example, in certain synapses the binding of a neurotransmitter named acetylcholine opens sodium channels. The Ligand gated channels are in usually selective for monovalent ions, and the ligands that regulate the channel activity are commonly refered to as neurotransmitters (i.e. acetylcholine, glutamate and glycine). Ligand gated channels are essential for maintaining the continuity of an action potential across the neuron, and for transmitting or inhibiting a signal between neurons through the synaptic connections. At the synapses the ligand gated channels are controlled by the fast chemical transmission of neurotransmitters; and this whole process is called facility diffusion.
Mechanically gated channels: These types of ionic channels are activated by changes in pressure induced by the gradient concentration. These channels follow simple diffusion because only the size and the concentration of ions and not the polarity of the molecules influence the diffusion process. So it is possible to say that this type of channel is activated only by the difference in the intercellular and extracellular concentrations or by osmotic pressure induced by changes in the cellular membrane due to the increase in size of the cellular volume.
Voltage gated channels: This type of ion channel opens and closes in response to changes in the surrounding electrical environment (measured in volts). Voltage gated channels are very important in the formation of an action potential, which requires two different types of ion transportation mechanisms (facilitated diffusion and active transport). The difference between these two mechanisms of transportation is that the first one requires a specific protein for each Cl-, Na+, K+ ion. While, the second only requires either one large polar
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molecule passing at a time, or several small polar molecules crossing the ionic channel at the same time. A good example of this type of transporter is the sodium-potassium ATPase which is responsible for returning the membrane to its steady state potential as was explained in sec. 1.2. The two-pore domain potassium channel is a good example of facilitated diffusion controlled by a voltage gated channel. Potassium channel: The behavior of this type of channel is determined by a concentration gradient producing a potential difference in the cell, which determines if the pore will open or close. The molecular arrangement of the channel results in its selectivity towards only potassium ions. If a high number of ions cross the protein the possibility of a larger opening of the channel increases. This property explains why the channel opens at the beginning of the action potential and closes when increases the possibility of the income of sodium ions. As is shown in figure 1.8.
Fig. 1-8 K+ and Na+ channels behaviour [1]
There are structural differences among the potassium channels, which give rise to the presence of several different families. These families are differentiated by the number of pores and the number of transmembrane. Some of the most characteristic families are: potassium channels with 6 transmembrane segments and one pore (6TM-1P), potassium channel with 2 transmembrane segments and one pore (2 TM-1P) and potassium channel with 4 transmembrane segments and 2 pores (4 TM-1P). The channel (6TM-1P) is voltage dependent having 6 domains and one pore. The voltage sensor is located in one of these segments. This channel is shown in figure 1.9.
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Fig. 1-9: 6 segments of the 6TM-1P are shown where the S4 segment functions as the voltage sensor
[14].
The 2TM-1P channel is recognized because it can be generated by two different type of genes. Although they can be voltage dependent, they act like delay rectifier, which means that they transport current in a much more efficient way from the outside/in than from the inside/out. They are also characterized for being open under equilibrium conditions of the action potential.
Fig. 1-10 Potassium channel with delayed rectifier and its domains.
To the right there are some members of this channel [14].
The 4TM-2P channel is characterized by having two pores or cavities in the same protein and containing 4 subunits. This type of channels was the last to be discovered and have the most number of members. Some of them are voltage dependent and others are slow rectifiers needing an agonist or ligand to be able to open or close. In this family we can find different channels like TREK and TASK.
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Fig. 1-11 Shows some families of (4TM-2P), and its unfolded structure [14]. The differences among members of this family are based in the type of activation of the channel. Two examples of this difference are: 1) the TWIK channel, which works as an internal rectifier like the 2TM-1P channels, and 2) the TASK and TREK channels, which are activated by the presence of large quantities of hydrogenous particles inside the cell. The TASK and TREK channels can also be activated by the presence of volatile anaesthetics such as halothane, isoflurano and chloroform, and are inhibited by local anesthetics such as bupivacina, meperidina and ropivocaina. The last member (TRAAK) is modulated by araquidonic acid and is not blocked by TEA or 4-aminopiridina [1]. This last group of channels is the subject of this thesis focusing in TASK and TREK channels.
1.4 PHYSICAL CONTEXT
In order to fully understand the behaviour of ion channels, we present in more detail the electrochemical behaviour of the neuron, focusing on the physical aspects that regulate the electrical behaviour of neuronal membranes As was mentioned in Sec. 1.1 the membrane can be studied as a circuit. If the membrane follows this basic feature of an electric circuit, the total membrane current (IM) would be the sum of the different currents in the system. More specifically, IM is the sum of the currents carried by ions crossing through the ion channels (Iion) and the current carried by ions moving outside the membrane which serve the function of charging and discharging the electric capacitor (CM). This relation is described by equation 1.1 where the general circuit model for a cellular membrane is shown [7].
( , ) IM ion M dEC I E t dt
+ = (1.1)
where E is the difference between the internal external potentials (E = Ei – Eo).
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1.4.1 THE MEMBRANE AS AN ELECTRIC CIRCUIT
For the study of ion channel behaviour it is necessary to have a clear understanding of Ohm’s law, which presents a relationship between the voltage and the electrical charge movement. The current that flows through an element is directly proportional to the applied voltage, where the voltage is the difference in potential energy between two charged points. At the same time, the current is inversely proportionally to the circuit resistance. We can therefore write the following familiar relationship [8].
V IR= (1.2) where V is the voltage measured in Volts (V), I is the current measured in amperes (A) and R is the resistance measured in Ohms (). In the same manner, the resistance can be described in conductance terms as:
1g R
= (1.3)
The membrane can therefore be modelled as an electric circuit, where the ionic channels act as resistors. Each ionic channel can therefore be characterized by a conductance so that the sum in parallel of each channel represents the total conductance of the membrane.
On the other hand, the membrane acts as an insulator, resisting the flow of charges across the membrane, and having the property of polarizing in the same manner as a capacitor, where the capacitor is an element that stores energy mainly due to a charge difference between two plates separated by a small distance. The capacitance is therefore a measure of how much charge is needed to be transported from one plate to another in order to induce a defined difference potential. The lipid membrane is therefore represented by a parallel plate capacitor of area A where the two plates are separated a distance d by a dielectric material characterized by one constant (ε). The cellular membrane capacitance can be written as:
o A QC d E
εε = = (1.4)
Where εo is the polarization of free space (8.85 x 10-12 CV-1m-1), d is the
thickness of the bilayer part (2.3 nm) and a hydrocarbon dielectric constant of 2.1 is assumed, referring to an area of 1 cm2. Q is the charge and E is the potential difference within the plates. By the definition of capacitance, it is found that the behaviour of the capacitor potential under the influence of an external current IC is written as:
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= (1.5)
In this way, we can find the time behaviour of the membrane in small
current changes with the previous equation. Ohm’s law will be used to replace the external current, obtaining the following equation:
dE E dt RC
Working out this differential equation the voltage behaviour is obtained
declining in time as shown in the following equation:
0 0exp expt tE E E RC τ
= − = −
(1.7)
Where E0 is the initial voltage, t the time in seconds, and in the case of the
membrane τ = τM is the time in which the voltage has declined to 37% of E0, also refereed to as the time constant of the membrane. In this way in an experimental form one can obtain the time constant by measuring the changes of the membrane potential through a microelectrode and adding small quantities of current through other microelectrodes during a determine period of time. Records of this method are shown in Fig 1.12.
Fig. 1-12 Shows polarization (A) and hiperpolarization (B) of neurons in the Lymnaea Stagnalis with external currents of 1nA, generating the charge and the experimental discharge of the cellular membrane.
A
B
22
In this way having the value of τM in an experimental way and knowing that the membrane capacitance is approximately 1µf/cm2 [8], it is possible to find an estimation of the membrane ionic current, obtaining in this way the number of ionic channels that are opened in the membrane. See sec 1.4.4 to have a fully understanding of this method.
1.4.2 THE NERNST EQUATION The resting potential is a key concept in the study of the membrane electrical behaviour. For this reason, our objective is to generalize how to obtain the resting potential for any ion, then focusing on potassium ions. In order to reach our objective it is important to study the Nernst equation, in which the concentration differences in the membrane, is the basis for finding an expression for the potential difference in the membrane in its resting state This resting state is based on a balance between the chemical potential and the electrical potential of the neuron. This electrochemical equilibrium can be characterized by the Nernst equation [8]. The chemical potential is induced by the ion concentration gradient. There is a tendency of the ions to move down its concentration gradient across the membrane. On the other hand, the electrical potential induced by the electrostatic force of the charge separation across the membrane tends to move ions in a direction determined by its particular charge. A balance between these two potentials determines the electrochemical resting potential. One example can be the flow of chlorine ions through the nongated chloride channels; chloride ions concentrated in the outside of the cell have a tendency to move inside down their concentration gradient. In addition, chloride ions tend to be pushed out of the cell due to the relative excess of negative charges inside the membrane. Depending on the existing membrane potential a ratio of intracellular and extracellular concentrations of chlorine ions is reached. The same occurs for potassium ions.
As mentioned before, the ionic current is driven by differences in ionic concentration across the membrane. Due to the concentration difference of these ions, water is absorbed into the cell resulting in an osmotic pressure. Therefore, osmotic work is necessary to move ions across their chemical potential, For dilute systems this behaviour can be modelled by the ideal gas law, where the osmotic pressure is equivalent to the pressure excerted by an ideal gas [8].
The ideal gas is described by:
PV NRT= (1.8) In this way a expression for the osmotic pressure can be found:
[ ]sRTnP RT S V
[ ] snS V
= (1.10)
In which we can find a voltage difference across the cell due to its ions concentration.
2
= − (1.11)
Since the work made for a gas is defined as: d PdVω = − (1.12) We can replace equation (1.9) and (1.11) in equation (1.12) and we have:
2
ω = (1.13)
Therefore, the work done per mol to change from [S] to[S] + d[S] is:
[ ] [ ]s
Integrating we obtain (1.14):
=
[ ] [ ]
SRTLog S
ω = (1.17)
Now, to describe the electrical potential, is quite easier since the work that
is necessary to transport a charged substance across a region defined by a
24
potential is ε is: e sZ Fω ε= (1.18)
Where ZsF is the number of charges carried per mol (Joules per mol)
Given that the electrical and chemical potential are know, the resting electrochemical potential can be found. s e oµ ω ω = + (1.19)
Replacing the equations (1.17) and (1.18) into the previous equation we
have:
µ ε = + (1.20)
[ ] [ ]
ε = − (1.21)
However, this model of the resting electrochemical potential is limited by
the fact that the equation (1.21) takes into account only one type of ion. For example, the electrochemical resting potential for a potassium ion is as follow.
[ ]58 [ ]
1.4.3 THE GOLDMAN EQUATION
In addition to the limitation that the Nernst equation only involves one type of ion, it also assumed that the potential difference has to be cero in order to obtain the resting potential. However, Goldmnan took a more accurate assumption based on the fact that different types of ions generate different flows across the membrane with a total flow of ions is constant but not cero. These different electric currents should generate a constant total flow in order to obtain the resting electrochemical potential. Therefore, it is important to find an equation that describes this potential taking into account the different kinds of ions involved in this process. Assuming the membrane as a capacitor of thickness L, where a concentration is fixed as [S]i in x = 0 and [S]o in x=L, the flow of ions
25
induced by the electrical potential is given by the Planck’s equation [8]:
[ ]zJ u S z
φ= − ∇ (1.23)
Where u is the mobility of the ion, which is the ion’s velocity in relation to a
constant electrical flow, φ is the electrical potential and ∇φ is the electric field, z is the valence and therefore z/|z| gives the direction of the force acting on the ion.
At the same time, we can relate the mobility of the ion u with the Fick’s diffusion constant given by Einstein. Where R is the universal gas constant, T is the absolute temperature and F is Faraday’s constant.
uRTD z F
= (1.24)
In this way, the density current flow of ions caused by the electric potential
is of the form:
φ = − (1.25)
Where the electric field is constant across the membrane d V dx L φ = − , with V as the
membrane potential. On the other hand, the density current flow caused by the concentration
gradient is given by:
− + = (1.27)
The solution for this equation is:
exp [ ]( ) exp 1 [ ]i zVFx RTL zVFxS x S RTL DzVF RTL
µ− − = − − + (1.28)
26
[ ] [ ] exp
− − =
− −
(1.29)
This flow of density current causes an electric current given by I ZFJ= .
Therefore, the Goldman-Hodgkin-Katz (GHK) equation can be found:
/2 2
s s FZ RT
ε
ε
ε −
As was mentioned beforehand, we pretend to find the electrochemical
resting potential involving several kinds of ions. Therefore, the sum of the currents must be equal to cero: 0
Na K Cl I I I+ + −+ + = (1.31)
Solving 1.31 for each ion and then solving together to obtain the potential, we have:
GHK Potential
K i na i Cl o
P K P Na P ClRT Log F P K P Na P Cl
ε + +
= + + (1.32)
1.4.4 THE HODGKIN AND HUXLEY MODEL (HH)
It is important to model how the channels open and close as a function of the voltage. This section will show that the changes presented in the membrane potentials cause the opening and closing of the ionic channels. This is the basis for electric excitability and in the same manner, it is the fundamental idea of neurophysiology.
Changes in the membrane potential can be produced by a large variety of external agents such as, electric currents, chemical products, and so on. Usually in experimental work, the stimulation is made by brief electric discharges to the neuron. This can be done by using small wires called microelectrodes. At the same time, the neuron response is registered by measuring the voltage changes with the use of a voltmeter connected to the neuron by another microelectrode. Another possible experimental protocol is to control the voltage and measure
27
variations in the current. Many different protocols are used to minimize the capacitance current and therefore, measure directly the current carried by ions crossing the specific channels. This technique is called “Voltage Clamp” which has been the most successful technique used in biophysics for the study of ion channels. This technique provides the basis for solving the dynamics of the conductance. A battery must to be used in order to maintain the membrane potential constant and monitor the currents. A current will flow form the battery in order to offset any current flowing across the membrane therefore maintaining the membrane potential constant. If we come back to equation 1.1 [7], we will see that for the voltage clamp the membrane potential dE dt is cero. Since the capacitor current Ic becomes cero once the membrane potential change has finished, the measured current is then only the current given by ion flow through the channel (Ii) as a function of time. This technique allows us to determine the flow direction of ions. Reversal potential of an ion channel (ENa for Na+) is the voltage at which no current flows through that channel. If the membrane is clamped at ENa, the Na+ channels should not contribute to the measured membrane current. Current carried by Na+ ions should be inward for potentials below ENa and outward to potentials above ENa. Therefore, if it is observed that the current reverses in the vicinity of ENa it is very probable that the current is dominated by the flow of Na+ ions. In the same way, the other ion flows (i.e. K+, Ca2+, Cl-) can be analyzed based on the reversal potential. Indeed, the flows of different ion species are independent from each other. This ion channel feature was called by Hodgking and Huxley as an “independence relation”.
In 1952 Hodking and Huxley tested two principal ion currents in the squid giant axon and consequently in many other nerve cells. These were the sodium (INa) and potassium (Ik) ion current. In addition, however they found one small ion current, called leakage current (IL), which is given by other ion species, for example the chloride current. Fig. 1.13 presents the changes in the circuit representation shown in section 1.2 based on the new assumptions by Hodking and Huxley [7].
28
Fig. 1-13 Shows the Hodking-Huxley model [7].
The low extracellular Na+ levels can affect the amplitude and direction of sodium current. However, variations in extracellular Na+ concentrations do not affect the ion flow through the potassium channels. Therefore, the currents given by potassium and sodium ions are completely independent, it is important to characterize the ionic permeability in the membrane. In the previous sections we have based our studies in Ohm’s law, which shows a linear relationship between the membrane potential and the ionic currents. However, for Ohm’s law to be valid, measurements have to be carried out a constant permeability. In order to do this, Hodking and Huxley measured what they called “Instantaneous current- voltage relation”. First, the axon is depolarized until the permeability increases, then, the voltage is changed by steps. Finally, the current is measured for a period of 10 to 30µs before the permeability of the ion can change due to the change in voltage. This experiment has to be done first for high Na+ conductance to obtain the Na+ conductance, then for high K+ conductance to obtain the K+ conductance. Therefore, the following equations to describe the ionic conductance apply:
Na Na
(1.34)
The I-V curves for Na+ y K+ ion openings are approximately linear in the
squid giant axon, so that the equation (1.1) is in the form of equation 1.41. However, currently it is known that the linearity of this curve is only an approximation, since the linearity of the curve can be affected by different factors, such us asymmetry in the ion and channel concentration. Therefore, the next equation shows the Ohm’s law involving the conductance and reversal potential of each ion.
29
( ) ( ) ( )Na NA K K L L app dECm g E E g E E g E E I dt
= − − − − − − + (1.35)
Where Iapp is the applied current. During an action potential there exists a flow of sodium towards the interior of 3.9 pmoles/cm2 and an external potassium flow of 4.8 pmoles/cm2. Given that these quantities are small, it is assumed that the ionic concentration and at the same time the reversal potential is constant and is not affected by action potentials. The previous equation can be rewritten in a more precise way as:
( )M eff eq app dEC g E E I dt
= − − + (1.36)
Where eff Na K Lg = g + g + g and eqE is the membrane resting potential defined as eq Na Na K K L L eff = (g + g + g )/g E E E E at the same time it is the balance between the reversal potential for three ionic currents. As a result when the cell is in a state of rest the conductance of the sodium and leakage are small in comparison with the potassium conductance, in this way the resting potential is very close to the potassium reversal potential. However, if the measured current is INa this would be reversible at ENa or if the current measured is IK this would be reversible at EK. Therefore, using the Voltage Clamp technique it is possible to measure the change in the capacitance of the potassium and sodium channels, as we can see in Fig. 1.14. In addition, using pharmacologic treatments this behaviour can be manipulated in a way that makes the curves move up or down (hiperpolarization or depolarization respectively). Since the pharmacological treatment is specific to each channel, we can determine the activation or inactivation of each ion channel independently. Activation is a fast process that opens the ion channels during a depolarization. When the depolarization pulse has finished in the activation process the channel returns rapidly to its reversal potential. On the other hand, inactivation is a fast process that closes the ion channels during depolarization, however, inactivation is only removed by hyperpolarizing the membrane in order to make it returns to its reversible potential.
30
a) b)
Fig. 1-14: a) shows the potassium and sodium conductance in function of time. b) I Vs E [7] 1.4.4.1 THE POTASSIUM CONDUCTANCE
As mentioned before the conductance of sodium and potassium gNa and gK, respectively are separable. Therefore, the conductance are described by the maximum conductance multiplied by a constant that changes between 0 and 1. In the model of capacitance, the change depends only on the voltage and time and not on the respective potassium or sodium ion concentrations nor on the direction of the current flow. For a fixed voltage, the conductance is time dependent. First, gK increases (depolarization) in a sigmoidal manner. Then, gK decreases (hiperpolarization) following an exponential behaviour, as we can see in Fig. 1.14. Therefore, this plot can be describe by a differential equation as follows [7],
( , )Kdg f E t dt
= (1.37)
where E is the difference between the membrane potential (E) and the resting potential (Eeq). Hodgking and Huxley showed that the K+ channels open by the intervention of many independent membrane-bound particles. In order to understand this theory, we suppose that the K+ channel has four identical particles each one with a probability n to attach to the correct position to induce the potassium channel to open. Therefore, the probability of finding all four particles in an open conformation is n4 (since this was the smallest exponent that
31
gave acceptable agreement with experimental data, this constant was chosen). Since the opening of potassium channels was found to be dependant on the membrane potential, the hypothetical particles were assumed to be charged.
A simple model assumes that the potassium channel can exist only in an opened or closed state (as mentioned before no intermediate states exist). Taking into account these assumptions, the change of n (to opened or closed channel) depends of the voltage and time as follows:
n
β (1.38)
Therefore, it is assumed that each particle moves between the permitted
and not permitted position. When the membrane potential has changed, the particles distribution (n) tends to move to a new value exponentially. In Fig. 1.16 we can observe that n4 is the adequate value to describe the potassium channel behaviour. Since n4 increases in a sigmoidal manner this fits very well with the slow increase of gK when the neuron is depolarized. In addition, when n4
decreases exponentially it describes correctly the decrease of gK when the neuron is hyperpolarized. For a more thorough understanding of this, we can focus on the ecuacion describing the current behavior (IK) in the HH model. This equation is basically the same as Ohm’s law but solving for I in terms of de conductance described beforehand,
4 ( )K K KI n g E E= − (1.39) where 4
k kg g n= . Taking into account that the proportion of closed channels (C) is 1- n and n
denotes the proportion of channels in an opened state (O). The previously mentioned particles make a transition between the permissible and non permissible state by a voltage dependent transition rate αn and βn. Given that, if the initial value n of the probability is known, the subsequent values can be found. Therefore, a differential equation of the change rate of n can be written like this:
(1 )n n dn n n dt
α β= − − (1.40)
An alternative is to used the time dependent time constant τn and the state
equilibrium value n∞ in function of αn and βn
1
(1.42)
32
Fig. 1.15 shows us the behaviour of τn and n∞. The relaxation time constant is maximum near the resting potential. In agreement with the τn curve, the constant time stabilizes at a slow rate to -75 mV (large time constant) and at a fast rate to +50 mV (small time constant).
Fig. 1-15 Shows the τn and n∞ plots [7]
Therefore, we can observe that for a negative membrane potential such as -75mV, the value of n∞ is small and the channel tends to close. On the other hand, for a positive membrane potential like +50mV, the value of n∞ is near 1 and the potassium channels tends to open. Therefore, the changes of n as a function of time can be found solving equation 1.40. We will express the aforementioned equation in terms of τn and n∞ replacing the equations 1.41 and 1.42 as follows:
( )n n n n n n dn n n n dt
α α β α α β= − − = − +
( ) ( )
ndn dt
+ = − + + +
( )( )n n dn n n dt
α β∞= − +
Therefore, equation 1.44 can be replaced in the last equation, having and
33
expression to find the changes of n across the time.
n
∞ −= (1.45)
Therefore, solving equation 1.45 we can characterize the parameter of HH
model for the potassium channel. In order to solve the depolarization event it is assumed that time is cero, E increases form 0 to E0 and then it remains constant. Suppose as well that E(0) = 0 . In this manner the sigmoidal increase is given by,
( ) 1 exp n
(1.46)
And the hyperpolarization is given by decreasing of E from E0 to 0 and is the form of
( ) exp n
(1.47)
Having these two equations and raising it to the four power we can now plot the HH parameter for potassium channel as see in Fig 1.16.
Fig. 1-16 Hypothetic representation of polarization and hyperpolarization [7].
Where the n plots to the left side are the polarization response, and the n plots to the right side are the hyperporalization response.
1.5 ANAESTHESIA
34
concentration, drug action mechanism and drug pharmacological effects. Many anesthetic properties can be explained by the receptor theory. A receptor is a cell component that interacts selectively with extracellular elements, and the quantitative relationship between drug dose and drug effects can be explained in relation to the interaction between a drug and its receptor. The receptor theory can also explain other properties such as selective activity effects and the specific pharmacologic activity of an agonist receptor [6].
An agonist is a drug that can become bound to a receptor on a cell in order to produce a physiological reaction. This interaction can either inhibit or activate the receptor. The activity of a drug is highly dependent on the affinity to its receptor, where the affinity is the measure of the compatibility between a drug and its receptor, When a drug has low affinity, the drug produces little or no effect. There are two kinds of agonist. One called full agonist which activates the receptor totally producing the highest activation level, and another one called partial agonist which activates a receptor partially producing inferior levels even with high doses. The difference between full and partial agonists is determined by the intrinsic efficacy of each drug. The drugs can present the same affinity for a receptor but they can also present different activation levels with the receptor. However the reasons of the different activation levels that are produced are still unknown.
Antagonists are drugs that bind to a receptor but do not produce any physiological response. An antagonist drug blocks the activity of an agonist by occupying its binding site. A competitive antagonist can be displaced by adding a high concentration of agonist, allowing the agonist to produce the expected effect independent of the presence of the antagonist. A noncompetitive antagonist binds to the receptor in an irreversible way, producing loss of the expected activity which cannot be restored by adding a high concentration of agonist. An.inverse agonist is one which causes an inhibition of the intrinsic activity of the receptor. In this case, the receptor increases or decreases the medicinal effect, acting like a “superantagonist” because it can induce a response to the drugs that is lower than the base line activity in the absence of the drug.
The receptors are located in different places within the cell, for example, in the cellular membrane, the cytoplasm or internal organelles. The physical structure of a receptor depends of the receptor type and its location. In general, the membrane receptors and nuclear receptors bind to ligands that cross the membrane looking for these receptors. The most important receptors for anaesthetics are cellular membrane proteins, which include membrane receptors, ligand-gated ion channels, and voltage-gated ion channels. Figure 1.17 shows where the drugs bind to each receptor.
35
Fig. 1-17 Schematic drawing of four types of membrane associated drug targets [6].
The different receptors described above are important in anaesthesiology. However, we focus only on anaesthetics that affect voltage-gated ion channels since these are the focus of the project. Local anaesthetics work by blocking voltage-gated sodium channels. Indeed, the drug is bound to the channel only when it is open and does not interfere in the opening and closing process of the channel. The drug only interferes with the actual flow of ionic current. General anaesthetics such as Halothane (See fig. 1.18), isoflurane, chloroform, inert gas xenon and more, produce reversible loss of consciousness through this blockage of ionic currents [2].
Fig. 1-18 Halothane Chemical Structure [3] The best way to calculate the potency of an anaesthetic is by using the
minimum alveolar concentration called MAC (EC50), which is the minimum concentration of a compound that anaesthetizes (defined as loss of response from a noxious stimulus) 50% of a given tested population. In order to determine the MAC in humans [3], it is necessary to make a surgical skin incision to test the noxious stimulus. In animals, this is done by clamping the tail or passing
36
electrical current through subcutaneous electrodes. The importance of MAC is that after a short number of tests we reach an equilibrium where MAC shows a direct correlation with the partial pressure of an anaesthetics in the nerve system. Macs for Lymnaea and human are shown in table 1.1.
Compound EC50 (uM) Animal Halothane 210 Human Halothane 590 Lymnaea Isoflurane 310 Human Isoflurane 710 Lymnaea Enflurane 520 Human Enflurane 570 Lymnaea
Sevoflurane 300 Human Tabla 1.1: Data calculated for Franks and Lieb 1993 [4].
Voltage gated channels are usually not sensible to clinical concentrations of general anaesthetics, and it is still unknown how blockage of the potassium current due to anaesthetics causes an inhibitory action. However, it is known that specific anaesthetics acting on the sodium channel cause and elevation in the spikes of the action potential which has important physiological implications. Also, the effects of anaesthetics such as Halothane is to hyperpolarize the neuron below the firing threshold of action potential as it is shown in Fig.1.19 Another of the main currents responsible for the action potential is the delayed rectifier K+ channel, which is only affected by a high concentration of volatile anaesthetics. The voltage gated calcium channel is almost insensible to general anaesthetics. Other receptors like ligand gated, GABA, neurotransmitter activated ion channel (i.e. Glutamate) [4] and others will not be studied in this project.
Fig. 1-19 Halothane hyperpolarize the spikes of action potential [3].
37
An example of anaesthetics in animals was discovered by Franks & Lieb
in 1988 [2], they discovered researching on Lymnaea Stagnalis neurons a potassium channel called two pore domain potassium, showing that this channel is characterized by being activated by volatile anaesthetics, and that these neurons showing sensitivity to anaesthetics, were found inside and outside the ganglion .
The anaesthetics can make the synaptic transmission unstable when they interfere with the release of a neurotransmitter. This interference is caused either by a change in the binding between the neurotransmitter and some specific location in the receptor, or by a change produced by the anaesthetics on the ionic conductance, which transports the electric activity to the receptor through the neurotransmitter. In this way the inhaled anaesthetics affect the synaptic terminals and the axon by modulating the ionic current through the different channels.
Anaesthetics can be combined with each other in order to study the nerve system. An example of this is the combination of halothane with zinc or copper used in this project. These two metals serve important physiological functions. They are found in the blood in a concentration of around 15uM. However there is a higher concentration of these metals in the brain of about 100uM. During the last few years scientists have discovered that these two metals can affect the ionic current of different channels like ligand gated and voltage gated channels. In 2001 Patel and Honore made an additional discovery regarding the two pore domain potassium channels, showing that these channels are activated by halothane. In 2004 Gruss et al. continued their research on the human version of this channel. They found that solutions applied with metal tip syringes caused a big inhibition in this particular channel. They found that this effect was caused by the content of zinc in the metal tip which is released when in contact with the test solution. Also, it was found that the channel is sensible to micromolar concentrations of copper. It is known that the TASK channels are inhibited by zinc and it has been shown that TASK-3 (KCNK9) and TREK-1 (KCNK2) are also sensitive to both metals. However, each one of them responds differently when different concentration levels of these metals are added. Our project has been developed based on the above discoveries. We pretend to characterize the 2 pore domain potassium channel in Lymnaea stagnalis by studying the reaction of the channel when mixers of halothane with zinc and mixers of halothane with copper are added at different concentrations . By studying the zinc and copper sensitivity of the Lymnaea channel, it is possible to determine its mammalian counterpart [3].
38
2 CHAPTER 2 – MATERIALS AND METHODS 2.1. AN INTRODUCTION TO VOLTAGE CLAMP TECHNIQUE
Voltage and current in neuron cells can be measured by 2 electrodes impelling the membrane cell. This method is called 2-microelectrode voltage- clamp technique explained as follows. For this procedure an Axoclamp 2A Machine (Axon Instruments, Foster City, California, USA) is used in order to control the voltage and to inject electrical current into the cell. First, two electrodes are inserted into a target cell. One electrode measures the voltage between the tip of the electrode and a reference (ground). The other electrode, injects current. Basically there are two modes of operating the Axoclamp equipment, Bridge mode and Voltage-Clamp mode.
In Bridge mode a cell membrane voltage is measured by both headstage amplifiers (HS-2 headstage, Axon instruments) which are connected to the electrodes. In the Voltage-clamp mode the cell membrane voltage is fixed at a constant value, one of them measuring the membrane voltage (headstage with gain 0.1, with an input of 1012, higher than the resistance of the electrodes used) and the other measuring the current transmitted through the membrane of the cell (headstage with gain 1, it passed about 600nA ). In this procedure it is required to keep the membrane voltage constant. This can be accomplished by using the first electrode to measure the membrane voltage and comparing it with an external supply command voltage (Vcom).
A current is induced by the difference between the external voltage and the membrane voltage, which is injected into the cell by the second electrode tending to reduce that potential difference until it becomes close to zero, as shown in Fig 2.1. To keep a constant membrane potential, the injected current needs to be equal to both the current crossing the membrane and the current inserted into the cell. In this way the cell current can be measured. The headstage is chosen deliberately with those figures in order to keep the levels of noise according to acceptable standards and to allow large currents to pass through an electrode. A higher gain allows more current to pass but it must be considered that this is at the expense of higher levels of noise. Of course, there are some natural limits imposed by the resistance of the electrodes.
39
Fig. 2-1 Circuit of 2-electrode voltage clamp technique. 2.2. ELECTRODES
Excellent electrodes are necessary to have a successful experiment. Electrodes are taken from borosilicate glass capillaries, Harvard apparatus (1.0mm external diameter x 0.58mm internal diameter and 7.5 cm long) using Campden Instruments model 753 microelectrode puller (see Fig 2.2a). Electrodes and electrode holders are filled with 2.5 M KCl ( See solutions chapter). This usually produces electrodes with resistances in the range 10 - 30 M. Electrodes with higher resistances are ruled out because this usually implies thinner electrodes which can prevent the delivery of the current and can easily be blocked. On the other hand, lower resistances can cause damage to the neuron. The electrode holder uses a Ag/Agcl pellet to change the ionic flow in the solution to electron flow in the wire (see fig 2.2b).
40
c)
Fig. 2-2 a) Microelectrode Puller, b) Enlargement of microelectrode puller c) Electrode holders.
Electrodes are mounted on hydraulic three axis micromanipulator (Headstage move, Narishige MO 203). The use of the manipulator allows accuracy in electrode positioning, preventing significant variation during the process. In order to prevent voltage offsets the neuron is placed into a perfusion table (this is an interchangeable solution table) which must be connected to ground, setting Vout to the ground.
In order to avoid the transmission of undesired ions from the (Ag/AgCl) pellet an alternate Agar bridge is used to connect the bath with a small circular chamber in which 2.5 M KCl solution is placed and where the pellet has been introduced. The other extreme of the pellet is electrically connected to the Axoclamp equipment setting to signal ground. (see fig 2.3).
41
Fig. 2-3 Shows the Perfusion Table
which has a important rectangular open channel of 4 mm wide, 1 mm deep and 15 mm long, at the end of the rectangular, a deeper circular chamber connected, from which the solution is sucked. At the other side,
perpendicular to the rectangular a 2 mm canal is connected, in order to allows the solutions flow. The ganglion is placed in the middle of the rectangular part, to obtain a correct bath.
The Agar bridge is taken from Pasteur pipettes that have to be heated in order to be shaped as an arch (measured about 1.5cm across with legs each about 1 cm long). The bridge is filled with an Agar solution which is prepared adding 1g of Agar in 99 g of GFSR (the composition of the GFSR will be described later). The experiment is mounted on a rig constructed inside a Faraday cage thus excluding electrical noise and mounted on a vibration isolation table (Model 22610 serial 842733, Micro-g Technical Manufacturing Corporation). The rig is grounded from a single point on the cage in order to elude any ground loop noise from currents generated by fluctuating external magnetic fields. 2.3. PERFUSION SYSTEM
In order to make the neuron study easier it is necessary to have a perfusion system that is made up of four 250 ml glass syringes containing the solutions (for a definition of the solutions see section 2.7) creating a dripping system providing the flow of the required solutions at any given moment.
At the end of the glass syringes a 23 gauge hypodermic needle is connected, together with the end of an independent Pasteur pipette, hermetically sealed. The tip of the pipette is then connected to a 2 mm polyethylene tube. A small silicon tube is used to make a transition between the polyethylene tube and the pipette. A polyethylene tubing is used due to its chemical inertness, its flexibility and the fact that it does not absorb small hydrophobic molecules such as anaesthetics. A short floating plastic disk must be used in each syringe containing volatile anaesthetic fluids in order to prevent evaporation.
It must be ensured that the four syringes have the same flow level in order to insure accurate results. To start the flowing of the solutions through the system a plastic syringe is placed at the end of the tubing which is used to pull the fluids through the network. Simply by counting the drops it easy to estimate solution
42
speed. Four syringes and three valves (all valves low-pressure, omni fit, from Anachem, Luton, Bedfordshire) were used as is shown in FIG 2.4a. The valves V1 and V2 allow a choice to be done between two different solutions, usually control (GSR) and a test solution of copper with halothane is controlled by V1 whilst halothane and a test solution of zinc with halothane is controlled by V2 (Fig 2.4b). The output of the V1 and V2 valves are connected by V3 for which one of the inputs goes to the perfusion table to make a bath and the other one goes to a waste recipient. In this way both control solutions and the test solution can be running simultaneously, allowing an easier and faster shift of solutions with a smaller probability of error, which can damage the cells. A capillary glass (the same glass used to make the electrodes) is located at a superficial angle at the edge of the circular part of the bath on the perfusion table. a) b)
Fig. 2-4 a) Shows the perfusion system including valves V1 and V2, b) Shows the V3 together with valves V1 and V2.
A polyethylene tubing is connected at the end of the glass and at the other side a 1 litre conical beaker is connected, where the solution is sucked to let a constant bath into the table by a water pump which is running at all times. That container is always partially empty to avoid electrical contact. Fig 2.5a shows the full electrophysiological setup and 2.5b a close-up of the perfusion table.
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a) b)
Fig. 2-5 a) Electrophysiology table and b) Perfusion table showing the impel and the full perfusion table including the glass used to suck the solution.
2.4. PREPARATION OF THE NEURAL TISSUE
Pound snails Lymnaea Stagnalis 25-35 mm in length (Blades Biological, Edinburgh, Ken) and a mass of 1.3 to 2.5 grams were purchased in groups of 50 to 100. These snails were kept in an aquarium of London tap water expose to air at 18C, with an air bubble generator that was constantly on. At least 24 hours before each new group of snails were put into the aquarium it was necessary to diminish the aquarium water level, clean the tank and refill with fresh water. The snails were fed with iceberg lettuce, reducing the amount of one large leaf twice weekly, the amount that they were fed varied with the number of snails that were in the tank. (See Fig 2.6)
Fig. 2-6 Tank used to keep the snails fed with Iceberg Lettuce
at 18C using London tab water.
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2.4.1. DISSECTION
Excess water from, the snail is removed with a paper towel and the snail is then weighed, this process occurs before dissection.
Using forceps about three quarters of the shell is removed, therefore exposing the body. The snail is put vertically on a Sylgarb slab and held down by exterior mantle that has been cut down the middle, in order to avoid dry out, normal saline solution is added (see solution section 2.7). A microscope was used from this point on in order to carry out the dissection process, the type of microscope that was used was Wild M8, Plan 1X (Heerbrugg, Switzerland) together with a Fibre optic lamp (Type 6834 FO, Philips) and light Euromex fibre optic light source EK-1 (Arnhem-Holland).
A three to four mm lengthwise incision is made along the length of the snail with microscissors through the middle of the dorsal surface of the snail, exposing the reddish buccal muscle extending the oesophagus and exposing the brain partially. The exposed muscle is put forward and held down. From the point of attachment the oesophagus is held tightly behind the brain and is cut further back from this point and held down next to the buccal muscle. All the tissue around the brain is removed, allowing the nerve connection to the rest of the body to be severed, therefore raising the brain.
Held down in the centre with the pedal ganglion facing up, the brain is then put in a separate drop of normal saline solution on the same Sylgard slab. The reddish colour of the pedal ganglia distinguishes them from all the other ganglia (Orange in colour) located under one of the pedal ganglia, the cell of interest is situated in the right parietal ganglia. The linking band of nerve tissue between the two pedal ganglia is cut and the ganglia is held down sideways, extending the brain and exposing the parietal ganglia .
Removed softly is the connecting tissue around the right parietal ganglion, where the nerve system is located. Referred to as yellow speckled cells these neurons are recognized by their distinctive appearance and position. The group usually is composed of three cells although sometimes there are 2 or 4. The ganglion presents two types of connection tissue. The first is the outer layer which consists of loose absorbent tissue that is easily sprained and could be removed away using forceps.
Second, a firmly suitable connective protective tube is softened by the application of Pronasse as a powder on the end of a pair of forceps. It is scattered over the ganglia to a concentration on the order 1mg per ml for around 20 minutes to loosen the ganglion membrane, this membrane looks like a balloon around the ganglion after the application of Pronasse. Then the right parietal ganglion nerve connection with the other ganglia is cut.
In order to isolate the right parietal ganglion, an incision is performed (left ganglion side), by taking away a small part of the right parietal ganglion in order to permit the later removal of the membrane that is left over. In a length of about
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0.5 mm to 1 mm the nerve root of the right parietal ganglion is cut. Long axons make the isolation of cell easier, since the brain is kept in position by this nerve root, therefore, the axon is not cut too short. See fig 2.7.
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Fig. 2-7 Shows the whole dissection procedure, until an isolated ganglion.
With the right parietal ganglia isolated, the tip of a Pasteur Pipette is filled up with normal saline and is used to suck the ganglia and transfer it to the perfusion table, always preventing any bubbles into the pipette and looking after the nerve system. In the perfusion table, a Pasteur Pipette is used to obtain a thin glass rod, approximately as big as the axon ganglion by heating the glass and pulling it as in Fig 2.8. This glass is used to hold the ganglia by its nerve root, at the opposite side of the pipette a long rubber tube is connected to suck the ganglion onto the holder.
Fig. 2-8 Shows the way to obtain a ganglion holder, by pulling the pipette until the necessary radius
is obtain. The right side is connected to a long rubber tube, used to suck the ganglion.
.
Fig. 2-9 Shows the ganglion held by the thin pipette.
2.5. ELECTROPHYSIOLOGY
Recordings are taken from one of these three to four cells, which are easy to be identified (in big snails). At the same time they are the weakest cells in the ganglion. For the first experiments performed, the records were taken from isolated neuron cells but in the following experiments it was shown that the record could be taken directly on the neuron in the intact ganglion with some changes explained shortly.
To isolate a single neuron it is necessary to remove the despicable cells by impelling the cell with a single electrode and pulling it away together with the cell. This is done in the case where the ganglion is not cleaned from the connective tissue and there are cells close to the cell of interest (usually in small snails). However, if the ganglion has plenty of loose cells or the ganglion is clean from the connection tissue, the neurons of interest have to be isolated without taking the unwanted cells.
To isolate a neuron it is impaled with two electrodes on opposite sides as close as possible to the axon for mechanical stability and the system is left for a couple of minutes to induce sealing (by the cell membrane) of the cell around the electrodes. The ganglion is then ready to be pulled back slowly by pulling the glass holder. With great care the cell would then continue to impale on the electrodes. (see Fig 2.10)
Fig. 2-10 Shows an isolated single neuron, hold by the two electrodes.
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This procedure is very difficult and has a low success rate. The possibility
of loosening the main cells increases with this procedure, and there is risk that an unwanted cell is removed. In addition, many times the ganglion becomes detached, which means that the procedure has to be repeated from the beginning. For these reasons we chose to perform the remaining experiments on the cells without removing them from the ganglion. This minimized the risk of damaging the main cells. To have stable records it is necessary to have as little trauma as possible on the cells by having extreme carefulness when the electrodes are impelled.
In order to improve the impelling procedure it was necessary to construct a voltage to frequency converter connected to two audio speakers. This converter is connected to the electrode signal and makes it possible to know, through an audibly signal, when the tip of either electrode has made contact with the cell. Some times the electrodes are impelled too deeply into the cell which can cause damage in the cell membrane. For this reason a buzz button is usually used on the Axoclamp to indicate when the electrodes are just touching the cell. A brief high frequency current is generated by that buzz button, and the duration of that current is fixed to 1 ms (the minimum current) in order to prevent cell damage. The next section explains the details about how the converter is built. (See fig 2.11)
Fig. 2-11 shows the neuron in the ganglion impelled by the two electrodes.
2.5.1. VOLTAGE TO FREQUENCY CONVERTER
To be able to have a good impel it is necessary to make a voltage to frequency converter [11]. To make the converter a LM331 ship was used, which is shown in Fig 2.12, and a LF411 ship was used to amplify the membrane potential ten times [12]. It was necessary to make two inputs in the converter to turn off or on either one of the electrode used, where the second electrode input represents the membrane current, and the first electrode input is the membrane voltage, which comes from the first electrode passing to the operational amplifier (see fig 2.13). The output signal is then connected to two audio speakers. This produces an audibly signal when each electrode is touching the cell.
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Fig. 2-12 A circuit for a voltage to frequency converter [11]
Fig. 2-13 A circuit for a ten times amplifier operational [12]
2.6. DATA ACQUISITION
The membrane potential Vmem is amplified by a factor of 10. At the same time Vmem is defined as, Vmem = Vin - Vout where Vin and Vout are the potentials measured inside and outside the cell, respectively. Using an 8 Pole Bessel filter was used (Frequency Device 902, Haverhill, Massachussetts, U.S.A) with an output gain of 0, 10 or 20 dB, giving a possible range between ± 25 nA (maximum gain) to ± 2.5 nA (minimum gain). In order to minimize the digitising errors in Analogue to Digital conversion the maximum possible gain is used, depending on the size of the current that is to be measured. For 20 dB, the minimum digitalized current step is about 0.001 nA, and the minimum noise of a model membrane (Clamp-1 model cell, Axon Instruments) was ± 0.003 nA. The membrane current is filtered at 10 Hz (using 10dB).
The command voltage input is scaled by a factor of 50, therefore 1 mV change in the command potential applied to the voltage clamp circuit is a consequence of a 50 mV change in the command potential input. The output of
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the Frequency Device is connected to a digital amplifier (DigiData 1200 Series Interface, analogue to digital converter card). This card operates with up to eight analogue inputs and two outputs, translating to a range of ± 125 mV for the membrane potential, and for the membrane current a range of ± 125 nA, to obtain a range of membrane potentials of ± 100 mV. The output channel for the command potential has a range of ± 5V, in practice the command potential is offset by -60 mV, giving a range between -160 mV to +40 mV. At 100 Hz, the output bandwidth of the voltage clamp is set.
The converter card is used to connect the Axoclamp equipment to an IBM- compatible PC (486, 25MHz). The data acquisition software was written by Ramin Nakisa, making it possible to record currents in nA and voltages in mV across the membrane as a function of time, therefore making it possible to measure I-V curves. But it is necessary to make sure that the voltage is changed slowly and constantly, to produce a steady state curve. The protocol used to measure the current as a function of the potential starts with the cell clamped at - -100 mV. Then a ramp of 3 mV per second is used.
The analogue to digital converter obtains a single analogue channel (an output connected to a command potential input on the Axoclamp) from two channels of data and output (the membrane current and potential outputs of the Axoclamp, respectively), providing information so that the acquisition programme can work.
Once a clear understanding of the protocol that is used for the voltage clamp has been made, it is important to know how the experiments are done in order to analyze the potassium channel reaction in each of the different solutions. The neuron is washed by the control solution when it is penetrated by two electrodes and the Axoclamp is in the bridge mode. In order to start obtaining information the Axoclamp is set to the voltage clamp mode. The duration of the ramp is approximately 2 minutes. Once the potassium channel behaviour has been obtained in its normal state, the solution is changed for halothane in order to obtain the second ramp. Since it is known that halothane activates the potassium channel, a change in the I-V curve should be noted. If the neuron is joined to the ganglion then it is necessary to perform the washing for four to five minutes, because the ganglion needs to be balanced by the solutions. The cells that are close to the one we are studying can affect the data if they are not perfused by the solution homogeneously. If the neuron is isolated, the washing that is needed in order to f