LITHUANIAN UNIVERSITY OF HEALTH SCIENCES (LSMU)

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LITHUANIAN UNIVERSITY OF HEALTH SCIENCES

(LSMU)

Recording of axonal action currents from rat cerebellar granule

cells

Physics, Mathematics and Biophysics department

Mohamad Jawhari, Medical Faculty, student 6

th

year

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1. SUMMARY

Author: Mohamad Jawhari; Supervisor: Prof. dr. Armuntas Baginskas. Title: Recording of axonal action currents from rat cerebellar granule cells.

Aim and objectives:

Aim: The aim of this research is to estimate the change of Na+ concentration in the thin unmyelinated ascending axons of cerebellar granule cells during action potential.

Objectives:

• To obtain recordings of axonal action currents from rat cerebellar granule cell by means of whole-cell patch clamp method in slices.

• To measure amplitude, duration, and backpropagation delay of the recorded action currents.

• To evaluate the change of intra-axonal sodium ionconcentration by using mathematical approach and measurement results.

• To discuss obtained results revealing their importance in neuroelectrophysiology.

This research work is a literature review that also included a revision and an overview of the patch clamp technique and its further refinements; moreover, there is short description of unmyielinated fibers electrophysiological properties with special focus on cerebellar granule cells. The obtained experimental results show that average amplitude and duration of axonal action currents measured in cerebellar granule cells are of -319 ± 35 pA and 0.72 ± 0.04 ms. The estimated increase of sodium ion concentration in the granule cell ascending axon during the action potential is equal to 0.174 mM, i. e. much smaller than the background level.

Summarized conclusion:

Based on the obtained results we conclude that: despite the very small diameter of the ascending/parallel fibers, the increase of the sodium concentration due to the propagation of a single action potential and burst of action potentials is much smaller than the background level of the sodium concentration.

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2. SUMMARY (Lithuanian/Lietuvių k.)

Autorius: Mohamad Jawhari; Darbo vadovas: Prof. dr. Armuntas Baginskas.

Pavadinimas: Aksoninių veikimo srovių žiurkių smegenėlių granulinėse ląstelėse tyrimas.

Tikslas ir uždaviniai:

Tikslas: Šio mokslinio tyrimo tikslas yra įvertinti natrio jonųkoncentracijos pokyčius smegenėlių granulių ląstelių nemielinizuotose aksonuose veikimo potencialo sklidimo metu.

Uždaviniai:

• Taikant whole-cell patch clamp metodą žiurkės smegenėlių riekelėse užrašyti aksonines veikimo sroves, sukeltas stimuliuojant lygiagrečiąsias skaidulas.

• Išmatuoti veikimo srovių amplitudę, trukmę ir atgalinio skidimo vėlavimą.

• Remiantis gautais duomenimis, taikant matematines formules, įvertinti natrio jonų koncentracijos aksono viduje pokyčius, sąlygojamus veikimo potencialo sklidimo.

• Aptarti gautus rezultatus, atskleidžiant jų svarbą neuroelektrofiziologijoje.

Šiame moksliniame darbe yra apžvelgta patch clamp eksperimentinė metodika ir naujausi jos patobulinimai; aprašytos plonų nemielinizuotu aksonų elektrofiziologinės savybės, ypatingą dėmesį skiriant smegenėlių granulinių ląstelių kylančiam aksonui ir lygiagrečioms skaiduloms. Remiantis gautais duomenimis, smegenėlių granulinėse ląstelėse registruojamų aksoninių veikimo srovių vidutinė amplitudė yra -319 ± 35 pA, o trukmė – 0.72 ± 0.04 ms. Tai leido įvertinti natrio jonų koncentracijos padidėjimą aksono viduje veikimo potencialo metu. Jis lygus apie 0.174 mM, t. y. žymiai mažesnis negu bazinis lygis.

Apibendrintos išvados:

Remiantis gautais rezultatais daroma išvada, kad nepaisant labai mažo kylančio aksono diametro natrio jonų koncentracijos padidėjimas aksono viduje veikimo potencialo ar jų pliūpsnio metu yra daug mažesnis už bazinį lygį.

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3. ACKNOWLEDGMENTS

I would like to express my deepest gratitude to my supervisor Prof. dr. Armuntas Baginskas for his essential advises and continuous support. The author is thankful for having an extraordinary supervisor, with remarkable patience and encouragement.

I reward a special thank for all the university doctors and stuff who provided the technical support in order to make this work easier to achieve.

Last but not least, my greatest love goes to my family that always supported me throughout life and during my studies.

4. CONFLICTS OF INTERESTS

The research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

5. CLEARANCE ISSUE BY ETHICS COMMITTEE

For this research we didn’t need permission from ethical committee. Prof Armuntas Baginskas did the experiments using the Prof. Morten Raastad research group equipment’s in the Basic Medical Science Institute at the university of Oslo.

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6. ABBREVIATIONS

V-clamp: voltage-clamp.

cAMP: Cyclic adenosine monophosphate. GABAergic: Inhibitory gamma-butyric acid. AIS: axon initial segment.

TZ: trigger zone. TTX: Tetrodotoxin. AP: action potential.

VSD: voltage-sensitive dye. GC: granule cell. HVA: high-voltage-activated. DAP: depolarizing afterpotential.

INaP: sodium ion persistent current.

INaT: sodium ion transient current.

CaCl2: Calcium chloride. Na2ATP: adenosine triphosphate.

NaCl: sodium chloride. CaCl2: calcium chloride

K-gluconate: potassium-gluconate. MgCl2: magnesium chloride.

NIH: national institute of health. EEC: European Economic Community.

KYNA: Kynurenic acid. CNQX: 6-cyano-7-Nitroquinoxaline-2,3-dione. KH2PO4: potassium dihydrogenphosphate

NaHCO3: sodium bicarbonate disodium salt hydrate.

HEPES: hydroxyethyl-piperazineethane-sulfonic acid buffer. Nav1 and Nav2: voltage-gated sodium channel family 1 and 2.

Nav1.2 and Nav1.6: voltage-gated sodium channel family 1, subfamily 2 and 6.

IR-DIC: infrared differential interference contrast. CA3 pyramidal neurons: Cornu Ammonis area 3.

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7. INTRODUCTION

Unmyelinated axons of the central nervous system, for example cerebellar parallel fibers [72; 88], hippocampal mossy fibers [12; 23], are very thin, having diameters of ~0.3 µm. The very small dimension of the axons can compromise a general belief (view) that membrane ion currents do not cause appreciable change in the intracellular (intra-axonal) ion concentration. This statement becomes invalid for sufficiently small diameters, since volume to surface ratio decreases proportionally to the diameter. The largest transmembrane currents flow during the propagation of action potentials. Thus, it would be relevant to estimate sodium concentration increase in thin unmyelinated axons during the generation of action potentials.

The whole-cell patch clamp recordings of the action currents propagated in the parallel/ascending fibers of the cerebellar granule cells have been carried out. Results of the experiment made it possible to evaluate the increase of the sodium ion concentration in the cerebellar ascending/parallel fibers during the propagation of action potentials.

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8. AIM AND OBJECTIVES

Aim: The aim of this research is to estimate the change of Na+ concentration in unmyelinated ascending axons of cerebellar granule cells during action potential.

Objectives:

• To obtain recordings of axonal action currents from rat cerebellar granule cell ascending axons by mean of whole-cell patch clamp in slice.

• To measure amplitude, duration, and backpropagation delay of the recorded action currents. • To calculate Na+ concentration change from recorded data by mean of mathematical equations. • To analyze and interpret obtained results in order to provide the readers with a clear discussion

part of the research.

This research work is a literature review that also included a revision and an overview of the patch clamp technique and its further refinements; moreover, there is simplified description of unmyielinated fibers electrophysiological properties with special focus on cerebellar granule cells.

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9. LITERATURE REVIEW

9.1. Patch-clamp:

Definition:

Patch-clamp means commanding a defined voltage ("voltage-clamp") on patch or cell membrane in order to quantify the resulting current, and determine the patch conductance. Clamping could also mean imposing a defined current through the membrane ("current-clamp") in order to measure the voltage across it [95].

Historical background:

Starting with Luigi Galvani’s pioneering work in the 18th century followed by the work of Emil du Bois-Reymond, Johannes Peter Müller and Hermann von Helmholtz in the 19th century, the membranes and cells excitability has always been the major interest for research on the nervous system [90].

In 1952,Alan Lloyd Hodgkin and Andrew Huxley revealed the ion channel events of action potentials by using the voltage-clamp technique. In 1963, they were awarded the Nobel Prize in Physiology and Medicine for their particular work. At that time, voltage-clamp was only applicable on big cells, as sharp microelectrodes were needed to penetrate the membrane [90].

For the first time in the late 1970s, Bert Sakmann and Erwin Neher resolved single channel currents across a membrane patch of a frog skeletal muscle by using the refined voltage-clamp technique. Then, they were also honored with the Nobel Prize in Physiology and Medicine (in 1991). [90]

The next breakthrough was the invention of the giga seal by Ernst Sakmann in 1980, which improved the signal-to-noise ratio and made the recording of even smaller currents possible. Nowadays, with the further refinements, this technique became one of the most important tools for the investigation of the behavior of single cells or whole cellular networks in the nervous system [90].

General principle:

The patch-clamp technique gained special interest in the research of excitable cells (neurons,

cardiomyocytes and muscle fibers) because it allows the investigation of a small set or even single ion channels [90].

A single ion channel conducts around 10 million ions per second, which generate current of only few picoamperes. Recording currents with such small magnitude is quite challenging not only for the researcher, but also for the equipment [90].

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In principle, this technique use thin glass or quartz pipettes with a blunt end to seal onto the membrane. Suction is applied to aid the development of a high-resistance seal in the gigaohm range. The tight seal obtained permits the electrical isolation of the membrane patch, which means that all ions fluxing the membrane patch flow into the pipette and are recorded by a chloride silver electrode connected to a highly sensitive electronic amplifier. A bath electrode is used to set the zero level [90].

To prevent alterations in the membrane potential, the amplifier generates a compensating current that resembles the current that is flowing through the membrane as a negative feedback mechanism.

The membrane potential of the cell is measured and compared to the command potential. In case of any differences between the command potential and the measurement, a current will be injected. This compensation current will be recorded and allows conclusions about the membrane conductance. The membrane potential can be manipulated independently of ionic currents giving the opportunity to investigate the current-voltage relationships of membrane channels [90].

Configurations:

Depending on the research interest, different configurations can be used.

There are four main methods in which a patch clamp experiment may be performed. These are: 1 Cell-attached configuration.

2 Whole cell configuration. 3 Outside-out configuration. 4 Inside-out configuration.

1-Cell-attached configuration:

In this configuration, the micropipette is brought into contact with the cell membrane, and a tight seal is formed by suction with the periphery of the micropipette tip. Once the seal has formed and suction released, all micropipette current has been eliminated except that flowing across the delineated membrane patch. Thus, the exchange of ions only occurs through ion channels embedded in the sealed membrane path and the inside of the micropipette. In view of the small size, only a very few channels may lie in the patch of membrane, and the opening of the channels even if it is one channel will lead to the flow of ions and formation of electric current [70; 82].

2-Whole cell configuration:

From the cell attached configuration that we just described the cell membrane within the micropipette is ruptured with a brief pulse of suction. Now the micropipette is in direct connection becomes to the inside of the cell while the gigaseal is maintained; hence it excludes leakage currents. The electric resistance

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must be in the range of 2-10 MΩ. In this situation the microelectrode measures the whole cell ion channels current. The technique is particularly applicable to small cells within the range of 5-20 µm in diameter, and provides good recordings [70; 82].

3-Outside-out configuration

The outside-out configuration is a microversion of the whole cell configuration that is obtained by pulling away the micropipette from the already ruptured cell. During withdrawal, a cytoplasmic bridge surrounded by membrane forms by pulling and becomes more and more narrow as the separation between pipette and cell increases until it collapses. This will result in obtaining an intact cell and a small piece of membrane, which is isolated and attached to the end of the micropipette. In this way we obtain an attached membrane "patch" in which the former cell exterior is on the outside and the former cell interior faces the inside of the micropipette. Now, the outside of the cell membrane may be exposed to different bathing solutions, and may be used to investigate the behavior of single ion channels activated by extracellular receptors [70; 82].

4-Inside-out configuration

In the inside-out configuration is obtained, without rupturing the membrane with a suction pulse, by pulling the micropipette from the cell-attached configuration. During withdrawal, as in the outside-out method, a cytoplasmic bridge surrounded by the membrane is pulled out from the cell. This bridge becomes more and more narrow and finally collapses leaving a vesicle inside the pipette. The obtained vesicle is not suitable for electric measurements. Just in a reverse way of the outside-out configuration, the part of the membrane outside the pipette may, however, be broken with a short exposure to air making the cytoplasmic side of the membrane becomes open to the outside. Inside-out patches can also be obtained directly without air exposure if the withdrawal is performed in Ca-free medium. With this configuration, the effect of a quick change in concentration on the cytoplasmic side of the membrane can be examined by changing the ionic concentrations in the bathing solution. Thus, this configuration can be used to investigate the cytoplasmic regulation of ion channels [70; 82].

Applications, advantages and disadvantages of each patch clamp configuration:

The cell-attached method is often used to study ligand-gated ion channels, channels that are modulated by metabotropic receptors, or neurotransmitters. This configuration provides direct contact between the compounds included in the pipette solution and the external surface of the membrane. This contact allows the accurate determination of concentration-response curves of the compound on ion channels studied. The main disadvantage of this method is that only one compound concentration in a concentration-response curve can be measured per patch [94].

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The whole cell method records the currents of multiple channels at once through a V-clamp. Moreover, it is possible to measures the membrane potential variation by switching to the current clamp mode. The advantage of this method is that it allows better electrical access to the inside of a cell because the larger opening tip of the electrode provides lower resistance. The disadvantage is that intracellular contents may be dialyzed by a large volume of the pipette solution [94].

The inside-out patch configuration provides the access to the intracellular surfaces of the ion channels. Using this method, the channels that are activated by the intracellular ligands can be studied and the concentration response curves of the ligands can be plotted [94].

The outside-out patch isolated from the cell, In comparison with the cell-attached configuration, can be used to examine the properties of an ion channel in am more convenient way by perfusing the same patch with different solutions. The entire concentration-response curve of a compound can be obtained in a single patch when the ion channels are activated from the extracellular face [94].

Finally, it is worth it to mention here the loose patch clamp as a different configuration from the patch clamps discussed above. In this configuration, a loose-seal interaction between the cell membrane and the rim of the glass microelectrode is achieved. This technique has the advantage that the pipette can be used repeatedly for recording in deferent locations while the cell membrane remains intact. The large leakage that occurs due to the loose seal is the major disadvantage of this method [94].

Perforated whole-cell patch-clamp:

Perforated whole-cell patch-clamp is considered as a variant of the patch-clamp technique by some literatures and an independent technique by others. It is used to measure the sum activity of ion channels across the plasma membrane of a single cell. The electrical access to the cell is obtained through inclusion of a pore-forming antibiotic in the patch pipette (for example, ionophore nystatin, amphotericin B, and gramicidin), which perforates the sealed patch of membrane in contact with the patch pipette. The pores obtained allow equilibration of small monovalent ions between the patch pipette and the cytosol. Moreover, by preventing the washout, it helps maintaining endogenous levels of divalent ions such as Ca2+ and signaling molecules such as cAMP, which make it ideal for studying ion channels whilst maintaining the integrity of second messenger signaling cascades. Also, it is superior to the conventional patch-clamp by reducing current rundown [61].

On the other hand, the perforated patch-clamp technique has two main disadvantages. First, the performer has to wait for about 10 minutes until pores form and a good recording is possible, which reduces the rate of successful recordings per time. Secondly, the access resistance is much higher than in conventional patch clamp recordings, which make the voltage control inferior in perforated patch recordings using

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patch clamp amplifiers. However, series resistance problems can be overcome by using a switch amplifier [73].

Planar and Lateral Patch Clamping:

In a planar patch clamping, the pipette is replaced with a micron-sized pore in a flat chip while in lateral patch clamping the pore is in the side wall of the channel. Moreover, the use of transparent chip in the lateral patch clamp can provide optical access to the patching site [66].

As illustrated in the Figure (1) below witch compares the three types of patch clamping techniques we can see that in both (lateral and planar patch clamping), the cell is positioned on the pore and suction is applied to facilitate gigaseal formation [66].

Figure (1)

On the other hand, planar and lateral patch clamping configurations need costly equipment such as a precise manipulator, a high-magnification microscope and an anti-vibration table when compared to conventional patch clamp [66].

The idea of bringing cells to the patching site instead of bringing the pipette to the cells gain the attention of many researchers that developed hundreds of different designs that have some advantages over each others [66].

Fertig et al. conducted one of the earliest attempts in planar patch clamping. During early attempt, the gigaseal quality was affected by the presence of debris in the solution that blocked or contaminated the one ring pore. For this reason, Stett et al. developed a concentric double pipette-like structure where its outer channel was used for cell positioning and its inner channel for current measurements. In this geometry of the pore, the Positive pressure was first applied in the inner channel to prevent debris from reaching its surface, and then the Suction in the outer channel brought the cell to the top of the

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measurement site. Once the cell is placed at the measurement site, a second suction in the inner channel will lead to seal formation [66].

The planar patch-clamp not only has the advantage to be used for automated whole-cell patch-clamp recordings but also its geometry offers more sensitive recordings of ionic currents and an increased accessibility of the membrane for optical and mechanical detection techniques. How this is achieved? To make more sensitive current recordings, reducing the capacitance of the electrode make the reduction in noise possible [11].

In planar patch clamping, the geometry of the electrode can be chosen more freely, than with pulling pipettes and adapted to minimize capacitance. Also, the planar patch-clamp made simultaneous use of electrophysiology and atomic force microscopy or some other scanning probe technique to study movement and shape changes in membrane proteins possible [11].

Automated patch-clamp technique:

The automated patch clamp technologies are divided into different categories based on the approaches used to form gigaohm seal. In this review we will discuss the two major categories:

1-Automated Glass Pipette-Based Patch Clamp:

This type of automated patch-clamp systems is based on the use of conventional electrodes to minimize the time-consumption of patching procedure and to achieve a higher throughput and reproducibility. In one approach, a pipette get contact to the surface of the cell that is suspended in one or more cell layers in a density-gradient solution or at the air/liquid interface. Then, gigaohm seal can be performed in order to achieve whole cell access or other patch clamp configurations same in the conventional manual patch clamp technique. In a second approach, a vertically upward pipette tip is positioned in the center of a polyimide sheet at the bottom of a well. Then, Suspension cells are added, and by applying negative pressure through the pipette tip, one cell becomes attracted and then attaches onto the opening of the pipette tip. In a third approach, gigaohm seal and whole-cell patch configuration are performed inside the micropipette tip, this approach Is achieved when first suspended cells flow through the glass pipette to the inside of the pipette’s tip [94].

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Figure. (2). The pipette electrode moves to contact the surface of a randomly chosen cell that is suspended in a layer within a density gradient (A) or at the air/liquid interface (B). (C) A cell is positioned on the recording pipette electrode using negative pressure at the suction channel. (D) Cells are flushed into a pipette and are pushed into the inside tip of the pipette [94].

However, there are still some drawbacks to the glass pipette-based automated patch clamp systems such as:

• Cells in suspension are required, similar as in the planar-based patch clamp technique. Moreover, these techniques are not applicable for tissue slices and none are capable of studying neural network dynamics [94].

• The cells are selected blindly, thus the quality of the suspension cells must be of both high quality and uniform [94].

• Parallel experiments of multiple cells are very challenging since the precise control of multiple simultaneous pipettes is complicated [94].

2- Micro-Fabricated Planar Electrode-Based Patch Clamp:

This technique use microfabrication such as silicon or plastic–based planar arrays owing micron-size holes for loose or tight seal formations. Several systems that employ this technique are commercially available, including Q-patch, NPC-16, CytoPatchTM, IonWorks (IonWorks HT and IonWorks Quatto),

and PatchXpress. The increase in throughput is the major advantage of the planar electrode-based patch clamp. Another advantage is the very low compound consumption due to the low volume of planar chips that make this method suitable for experiments that use rare and expensive compounds or limited amounts

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of compounds. Moreover, the compact size of the recording chips decreases the environmental electronic noise interference [94]. However, there are still some drawbacks within these systems:

• These techniques produce lower quality recording (usually with high leaking currents). This disadvantage limits the study of some channels, such as inwardly rectifying potassium channels and transient receptor channels since they express currents that are difficult to distinguish from nonspecific “leak” currents [94].

• There is less flexibility with cell types and more specificity with cell lines since these automated systems are fabricated according to industrial requirements but not according to flexibility required by academic researchers. For instance, some experiments such as precise patching onto multiple small structures in a preparation (e.g., the axon, dendrites, and soma of neurons) are technically demanding and still highly depending on the electrophysiologist skills using the manual patch clamp [94].

9.2.Patch-clamp in slice

:

History:

Years after the introduction of patch clamping, the intact cells in the central nervous system tissue were thought to be inaccessible for patch clamping because it was not yet possible to maintain the intact structure of brain tissue and achieve the clean cell membrane needed in order to form a gigohm seal between glass pipette and cell [49]. In the meantime neurons and glia were studied in primary culture that have several disadvantages such as changes in gene expression and synaptic connections, and even the identity of cells all become unknown factors [44].

Later, neurons and glia were studied after acute dissociation using enzymes such as papain or trypsin. Results from these studied showed that the enzymes used could alter the receptors or ion channels of interest; also synaptic transmission can be affected [44].

During the 1980s the techniques for recording from brain slices with intracellular electrodes were greatly improving, aided by the development of the discontinuous single electrode voltage clamp [41]. However, these recordings were still limited by the lower resolution of intracellular microelectrode recording [44]. The problems of cell isolation and signal resolution were overcome by the introduction of techniques to allow patch clamp recordings to be made from brain slices [37] and even from the in vivo brain [40; 71].

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Advantages:

Classically, whole-cell recording is performed in vitro either on brain slices, freshly dissociated neurons, or on cell culture models. When performed on neurons in brain slices, this technique presents several advantages as:

• Neurons can be studied to some extent in preserved brain circuits, and compared to cell culture preparations; it provides an environment that is physiologically relevant. This allows early capture and monitor cellular and molecular events that are triggered by any type of acute pharmacological manipulations (temporal resolution) [84].

• Adding fluorescent markers provided the capability to visually identify regions of interest in brain slices with high specificity and sensitivity [84].

• It offers the capability to access the intracellular space of the cell by opening a significant portion of the plasma membrane. This allows manipulating the content or concentration of specific ions composing the internal solution. Therefor, molecular targets or cellular mechanisms can be studied under different conditions. For example, upon establishing whole-cell configuration, any specific pharmacological agent (e.g., antagonists) that one can add to the recording micropipette (patch pipette) solution will directly diffuse into the cytoplasm and act on its specific intracellular targets without altering the target function in neighboring cells. Moreover, patch clamping in slices provided lower resistance, less competing noise, and thus better electrical access to the inside of the cell [84].

9.3.The cerebellum:

The cerebellum has always been seen as a distinct subdivision of the brain. Different researchers provided the accurate description of its gross appearance and major subdivisions. By the beginning of the 19th century, the classical descriptive anatomical work was completed, and experimental study of the functions of the cerebellum began. In this review we will have an overlook on cerebellar cytology, and the function of cells that shape local-circuits within the cerebellum.

Talking about the cytology of cerebellum, (Suzana Herculano-Houzel) [51] in her review: Coordinated Scaling of Cortical and Cerebellar Numbers of Neurons stated that the relative size of the cerebral cortex increases with brain size, but relative cerebellar size does not. The number of neurons in the cerebral cortex is directly correlated with the cognitive abilities across species than the absolute or relative size of the brain [51; 81]. For instance, the cerebral cortex (with the underlying white matter) represents 28% of

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total brain mass in the least shrew, 43% in the tree shrew, 66% in the marmoset, 76% in the macaque, 84% in humans, and 73% in the pilot whale [24; 53].

The cerebellum contains few cell types that are aggregated in the cerebellar gray matter including the cerebellar nuclei and cerebellar cortex, which is divided into three layers:

• The molecular layer formed by stellate and basket cells [69]. • The Purkinje layer formed by Purkinje and candelabrum cells [69].

• The granular layer formed by granule cells, Golgi cells, unipolar brush cells, and Lugaro cells [69].

Neurons of the cerebellar nuclei are located deeply inside the cerebellar white matter, and they are beyond our review focus. These cerebellar nuclei along with some vestibular nuclei form the major output of the cerebellum [33; 55].

Furthermore Cerebellar neurons can be classified into:

• Inhibitory gamma-butyric acid (GABAergic) Such as Purkinje cells, Candelabrum cells, and other cerebellar cortex GABAergic interneurons including basket and stellate cells in the molecular layer, and Golgi and Lugaro cells located in the granular layer [18; 59; 60].

• Excitatory glutamatergic neurons [15; 54] such as granule cells, unipolar brush cells, and excitatory projection neurons (large neurons in the cerebellar nuclei) [25; 85].

After listing different classifications of cerebellar cytology, now we will have a closer look on the cerebellar local-circuits. The cerebellum receives two major and one minor types of afferent input. Mossy fibers Arising from multiple sources in the central nervous system are the major afferent fibers to the cerebellum. They project to the Purkinje cells through granule cells/parallel fibers. Climbing fibers arise from the inferior olivary complex and they synapse on the dendrites of Purkinje cells. Third sets of afferents called neuromodulatory cerebellar afferents terminate in all three layers of the cerebellar cortex. All projections to the cerebellum send a direct branch to the cerebellar nuclei, which also receive the Purkinje cell input that are essential in monitoring the whole cerebellar output [50; 68].

Thus, the fundamental information-processing unit of the cerebellar cortex is the Purkinje cell, which integrates information from previously mentioned afferent inputs.

Mossy fibers synapse on granule cells in the granule cell layer of the cerebellar cortex. The cerebellar granule cells are widely held to be the most abundant class of neurons in the human brain. They give rise to ascending fibers that contact Purkinje cells. At the level of molecular layer of the cerebellar cortex, ascending fibers bifurcate to form T-shaped branches (parallel fibers) that also transmit information via

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excitatory synapses onto the dendritic spines of the Purkinje cells which branch extensively in a plane at right angles to the trajectory of the parallel fibers [75].

The Purkinje cells receive a direct modulatory input on their dendritic shafts from the climbing fibers, all of which arise in the inferior olive. Each Purkinje cell receives numerous synaptic contacts from a single climbing fiber. In most models of cerebellum function, the climbing fibers regulate movement by modulating the effectiveness of the mossy—parallel fiber connection with the Purkinje cells [75].

Since The Purkinje cells have GABAergic output, they will inhibit the firing of deep cerebellar nuclei which are the only output cells of the cerebellar cortex. However, the deep cerebellar nuclei receive excitatory input from the collaterals of the mossy and climbing fibers [75].

Diving more deep, beside Purkinje and granule cells, cerebellar local-circuits contain Candelabrum cells, and other cerebellar cortex GABAergic interneurons including basket and stellate cells in the molecular layer, and Golgi and Lugaro cells located in the granular layer. Less is known about the activity of these neurons of the cerebellar cortex. It is noteworthy that all of the other three cell types (Golgi, stellate and basket cells) are inhibitory. Each of these cell types is excited by the parallel fibers and each feeds onto a certain part of the circuit. Golgi cells, which have their soma in the granule layer, exert feedback inhibition to the granule cells through their apical dendrites in the molecular layer. Stellate cells receive inputs from the parallel fibers and provide an inhibitory input to the Purkinje cell dendrites. This inhibition may clear the activity of the Purkinje cells shortly after they have been excited, allowing the Purkinje cell to respond to only to the immediate activity in granule cells and parallel fibers. The basket cells are a special case, since their axons usually go to surrounding Purkinje cells, not the ones to which they are adjacent. This may "turn off" activity in Purkinje cells at a certain distance surrounding the focus of activity [21].

Finally, although there is some variation across the cortex, this is minor in relation to the scale of the uniformity. Thus, this basic circuit repeats throughout every subdivision of the cerebellum in all mammals, and it is considered the functional module of the cerebellum. Modulation of signal flow through these modules provides the basis of multiple tasks carried out by the cerebellum [6].

9.4. Electrophysiological properties of unmyelinated fibers and Granule cerebellar cells:

In order to understand the relevance of studying sodium ion concentration changes across the voltage clumped parallel fiber (whole cell patch clamp) during backward spikes propagation, we will have an overview on the ionic basis of action potential initiation and propagation in excitable neurons, the work of different ion channels especially sodium ones, and finally have a closer look on different neurons

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electrophysiological properties with special focus on granule cells. Action potential:

An action potential (or nerve impulse) is a transient alteration of the transmembrane voltage (or membrane potential) across the membrane of an excitable cell (such as a neuron). It is generated by the activity of voltage-gated ion channels embedded in the membrane [97].

Action potentials or spikes are initiated in the proximal anatomical region of the axon termed axon initial segment (AIS). The voltage threshold for spike initiation and the exact location and length of the spike trigger zone (TZ) within AIS, as well as the amplitude and waveform of the action potential in different neuronal classes, depend on the geometry (which is beyond our interest in this review) and passive electrical properties of a neuron as well as on the type, spatial distribution, and density of a variety of voltage-sensitive ionic channels [97].

The basis of action potential generation depends on the opening and subsequent inactivation of voltage-gated sodium channels, followed with a slight delay by opening of voltage-voltage-gated potassium channels. This interplay in opening and closing of sodium and potassium channels is not as simple as we illustrate and it depends on many other factors playing roles in the membrane electrophysiological properties such as maintaining concentration gradients across the membrane by sodium-potassium pumps. Here also we must mention that variation at molecular level of ionic channels such as the presence of 10 voltage-gated sodium channels (Nav1 and Nav2 families, that differ in means of voltage dependence, kinetic of opening and closing, and modulation of these gating properties), and its location along the axon affect membrane excitability [14].

For instance, the comparison between the response of Nav1.2 and Nav1.6 sodium currents to rapid repetitive depolarizations showed that Nav1.6 sodium currents have use-dependent potentiation while Nav 1.2 sodium currents have use-dependent reduction. Also, Nav1.6 currents expressed more resistant to inactivation in comparison to Nav1.2 [98].

The initiation of action potential needs a depolarizing event in order to open voltage –gated sodium channels. This depolarization can be achieved artificially by inserting a microelectrode into an axon and injecting current, or by extracellular stimulating axon with an electrode. Action potential originates at the point of lowest threshold, which is a function of the balance between sodium, potassium, and leak currents [14].

In general, it originates where sodium channels are clustered at high density, this is usually the axon hillock. Since we are interested in unmyelinated axon that are small in diameter, these neurons are loosely surrounded by glial cells or in some cases not covered such as parallel fibers in the cerebellar molecular

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layer. Moreover, there is evidence that neurons use different channel subtypes in subcellular regions of the cell. This would allow the cell to fine tune the excitability of the cell in different regions [14].

In particular situations, unmyelinated fibers express regions of high-density sodium channel clustering capable for regenerating the action potential. As an example, Engel and Jonas (2005) recorded directly from mossy fiber terminal boutons. Every bouton contains about 2000 sodium channels. Models suggest that those channels have faster inactivation kinetics than dentate granule somatic sodium channels, thus help regenerate the action potential at a location that otherwise, because of impedence mismatch with the axon, might prove a liability for propagation [38].

Conduction of the action potential along unmyelinated axons depends on the spread of current passively ahead of the active region. At the leading edge of the action potential, a rapid influx of sodium ions will lead to depolarization of a new segment of membrane towards threshold. At the following edge of the action potential, potassium channels are opened resulting in outflow current that return the membrane potential towards the resting value. The inactivation of voltage-gated Na+ channels and the high conductance state of hyperpolarizing K+ channels will make this piece of axonal membrane not excitable for a short period of time known as refractory period [14].

Conduction velocity in unmyelinated axons depends on several biophysical factors such as how much current is injected by the sodium channels, how far the current can spread longitudinally, and how quickly the adjacent membrane can be brought to threshold. Those factors in turn depend the number of available Na+ channels, membrane capacitance, internal impedance, and temperature [34].

First, since more sodium channels provide more current, it is thought that an increase conduction velocity is directly proportional to the increase in channel density. This hypothesis is applicable only for low to moderate sodium channel densities because the channels act as dipoles (the source of their voltage sensitivity) and add additional capacitance to the membrane. In general, the Conduction velocity can be diminished by lowering external Na+ concentration or by partially blocking Na+ channels with a low concentration of TTX. In addition, the larger the sodium current, the steeper the rate of rise of the action potential [34].

Second, the time required to charge the membrane is the product of the specific membrane resistance and capacitance. The membrane capacity is a reflection of the amount of charge stored on the membrane per unit area while resistance is the product of intra-axonal medium interactions. Thus, if the capacity is smaller then the time needed to reach threshold is shorter [34].

Finally, temperature affects the rate of increase of Na+ channel conductance because channels dynamics are slower at lower temperature, which in turn will affect the action potential waveform. In general conduction velocity in unmyelinated axons is slow. For example, it has been estimated to be close to 0.25

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m/s at Schaffer collateral or at the mossy-fiber axon, and reach 0.38 m/s in the axon of CA3 pyramidal neurons [34].

Action potential back propagation:

In opposition to the canonical forward propagation along the axon to the presynaptic terminals, action potentials can backpropagate and invade the soma up to the dendrites [43].

Here we should be aware of the difference between action potential backpropagation and antidromic propagation frequently used in electrical stimulation during experimental studies. When we stimulate an axon, two action potentials can be evoked, one will propagate from the point of stimulation towards the synaptic ending and another will travel towards the soma. Antidromic propagation refers to the direction of the action potential that moves towards the soma [43].

Since the 1950s, extra- and intracellular recordings in a variety of studies suggested that dendrites contained active conductance. The combination of patch pipette recording and infrared differential interference contrast (IR-DIC) optics in acute brain slices enabled the visualization and greatly facilitated direct measurement of action potentials (APs) in dendrites [92].

Dendritic recording, using either sharp microelectrode impalement [63] or the whole-cell variant of the patch-clamp technique [49; 87], is still the most direct approach available to measure dendritic electrophysiological properties [92].

Multiple recordings from the same cell can determine whether AP spread into the dendrite is active or passive. In reality, studies showed that dendritic properties is somewhere between these two extremes, supporting active backpropagation in which APs travel long distances through the dendritic arbors. Since both Passive spread and decremental (active) backpropagation decrease in amplitude with distance from the soma, it is confusing to differentiate between them. However, it is still possible to distinguish between them pharmacologically since active propagation relies on dendritic sodium channels. For instance, tetrodotoxin can block dendritic sodium channels, therefore attenuate actively backpropagating, but not passively spreading, APs [92].

Nowadays, fluorescence-imaging techniques are an excellent complement to direct recordings. For example, they were more widely used than direct recordings to study the basal and distal apical dendrites of pyramidal cells and interneuron dendrites [4; 45; 67]. Imaging depolarization with a fast voltage-sensitive dye (VSD) is another approach that is rarely used because (VSDs) offer a fairly poor signal-to-noise ratio and exhibit pronounced phototoxicity even in the absence of illumination [5]. Moreover, VSDs diffuse slowly along dendrites because they are membrane-associate dyes. Calcium indicators have been more widely used to image dendritic AP initiation and Propagation but they showed two major

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disadvantages when compared to direct recordings and voltage sensitive dyes. First, they lack the temporal resolution of electrophysiological and VSD techniques. Second, they only provide indirect measure of depolarization [92].

Finally, understanding the background of variations in backpropagation between different cell types and even between different dendrites of the same cell is still challenging for scientists. Obviously, based on different studies, electrical signals might be shaped by the structure of the dendrite and the interplay of passive and active membrane conductance, in another term, by the morphology and the presence (in term of location and densities) of dendritic ion channels [92].

Sodium channels and currents:

The voltage-dependent Na+ channels have three subunits (a, b1, b2) that were isolated with the use of a derivative of a scorpion toxin. The (a) subunit is a large glycoprotein, which has at least nine different isoforms, it is the building block of the water-filled pore of the ionic channel. The (b1), and (b2) subunits are smaller, and have some other role, such as in the regulation or structure of the native channel [19]. The (a) subunit of the Na+ channel contains four internal repetitions that contain each six hydrophobic domains spanning the membrane as an a-helix. The fourth (S4) hydrophobic domain has been proposed to be critical to the voltage sensitivity of the Na+ channels. Voltage-sensitive gating of Na+ channels is accomplished by the redistribution of ionic charge (“gating charge”) in the channel. Positive charges in the S4 region may act as voltage sensors such that an increase in the positivity of the inside of the cell results in a conformational change of the ionic channel [89].

The mechanisms of inactivation of ionic channels by blocking the inner mouth of the aqueous pore is probably not only directly achieved by changes in the membrane potential, but also is triggered or facilitated as a secondary consequence of activation. For instance, Site-directed mutagenesis or the use of antibodies has shown that the part of the molecule between regions III and IV may be allowed to move to block the cytoplasmic side of the ionic pore after the conformational change associated with activation [89].

Sodium channels can generate three types of sodium currents: (1) the fast-inactivating transient Na+ current, (2) the persistent Na+ current, which slowly activates and inactivates [26] and (3) the resurgent Na+ current which is activated upon repolarization in sub-threshold, potentials causing membrane depolarization and enabling the cell to fire at higher frequencies [76].

Most neurons express a high density of tetrodotoxin (TTX)-sensitive voltage-gated sodium channels, whose main function is to generate action potentials by carrying a large activating and

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rapidly-inactivating “transient” sodium current, activated when membrane voltage is depolarized above threshold (typically near −55 to −50 mV) [17].

Persistent sodium current is active near rest (65 mV) and do not inactivates even with quite strong depolarization. Thus, this persistent current participates in cellular excitability and in setting action potential threshold, in another way; it can affect the excitability and the shape of action potential. There is still a challenging concept whether the same channels mediate persistent and transient sodium currents [10; 26; 74]. This controversy began by the prediction of persistent sodium current by Hodgkin-Huxley models that overlap with the transient current at the voltage range in which steady-state activation and inactivation occurs. Persistent sodium currents have been identified both in the soma and dendrites [26]. Recently, persistent sodium currents showed tetrodotoxin sensitivity; application TTX blocked this current near the initial portion of the axon 10 – 40 m from layer 5 neocortical pyramidal neuron somas [8]. Persistent sodium currents are thought to play important role in the firing properties of at least some principal cell types within the hippocampus [16; 46; 91; 96].

Resurgent sodium currents are voltage-dependent and tetrodotoxin sensitive. Sodium channels open briefly and then become blocked by a voltage dependent open-channel blocker that, at negative potentials, will unbinds rapidly [77]. Thus, the resurgent sodium current flows briefly during repolarization because channels will be unblocked at this stage. Recent studies claimed that the cytoplasmic tail of the “4” accessory subunit is responsible for the properties of the resurgent sodium current in Purkinje cells [47]. These resurgent currents are present in many classes of fast-spiking neurons [10; 58].

Granule cells:

The most numerous neurons of the brain are the cerebellar granule cells. Granule cells, which are the only excitatory neurons of the cerebellum, have very simple geometry consisting of four short unbranched dendrites and a thin axon that branch into parallel fibers. Mossy fibers activate GCs, which emit their output to other neurons in the cerebellar cortex through parallel fibers. In turn, GCs receive feed-forward and feedback inhibition from Golgi cells. They were discovered by Camillo Golgi and Ramon y Cajal at the end of the nineteenth century. Their key position within the cerebellar-cortex circuitry forming the input layer of the major cerebellar afferent system made them the object of intensive investigation. The beginning was with the field recording of their activity in the 1960s, the discovery of their GABAergic inhibition and glutamatergic excitation, and the characterization of their membrane and synaptic mechanisms with patch-clamp techniques in the 1990s. Then in the last two decades, a series of electrophysiological and imaging studies have unveiled major yet undisclosed functional properties of

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granule cells leading to the rise of different hypothesis concerning the function of the whole cerebellar cortex [28].

Numerical simulations indicated the compact electrotonic structure of granule cells allowing excitatory postsynaptic potentials to diffuse with little attenuation from their dendrites to axon. Simultaneously, The spike arose along the whole axonal ascending branch and invaded the hillock. The invasion of axon hillock promoted spike back-propagation with marginal delay (<200 µs) and attenuation (<20 mV) into the somato-dendritic compartment. These findings indicate that granule cells are able to perform sub-millisecond coincidence detection of pre- and postsynaptic activity and to rapidly activate Purkinje cells contacted by the axonal ascending branch [35].

Although substantial knowledge has been accumulated on cerebellar granule cell voltage-dependent currents, their role in regulating electroresponsiveness has remained speculative

In general, a variety of voltage- and Ca2+-dependent channels generate ionic current flows and regulate membrane potential in neurons. Although some channels are involved primarily in generating action potentials, others influence subthreshold responses and rhythmicity [30; 62].

In the past decade, several studies have reported voltage-dependent membrane currents in granule cells in culture [27; 39; 52; 57; 79; 86] and in situ [9; 32; 80]. These studies revealed the presence of a transient tetrodotoxin (TTX)-sensitive Na+ current, multiple high-voltage–activated (HVA) Ca2+ currents, and multiple K+currents, including a fast-activating and a delayed-rectifier K+ current, a Ca2+-dependent K+current, and an inward rectifier K+ current. Despite the fact that those currents where identified, their relationship with the intrinsic excitable response has remained speculative [42]. Moreover, the involvement of persistent Na+ currents in controlling spike initiation did not get enough attention [2; 3; 30; 48]. This fact constituted the cornerstone for later conducted researches founding out that Voltage-dependent Na+ currents play an important role in shaping the intrinsic activity patterns (digital and analog) conducted by cerebellar neurons. Several studies such as: Current-clamp recordings in acute cerebellar slices [13; 29] and in vivo [20] concluded that granule cells not only act as regular spiking neurones in response to sustained, intense depolarizing stimuli, but also, they are able to conduct additional, peculiar patterns of activity and AP organization [30; 31] in the presence of just-‐ threshold depolarization.

Single APs are preceded by slow, ramp-like depolarizing prepotentials, and are often followed by transient depolarizing afterpotentials (DAPs) that may repeat before the other AP is fired. APs are not rhythmic and, tend to cluster into low-frequency bursts. These findings suggest the intervention of a

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persistent Na+ current [30], similar to INaP that in various neurons subtend sub- and near-threshold

sustained depolarizing events (discussed in [64]).

In a more elaborated explanation, when K+- and Ca2+-channel have been blocked, the steady-state voltage-current (V–I) relationship of GCs showed an inward rectification region at about −55 to −30 mV that is abolished by tetrodotoxin (TTx) [30]. Also, modelling data encouraged the view that the depolarizing envelope subtending AP bursts depends on INaP [31]. In addition, the presence of resurgent

Na+_{-current had been recently demonstrated in GCs [1], and had also been suggested to participate in GC}

AP clustering [31].

These findings indicated that besides INaT, persistent and resurgent Na+ currents were observed. The

determination of the biophysical and functional properties of these currents is still the subject of interest for many scientists in order to set the excitable properties of granule cells [65].

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10. RESEARCH METHODOLOGY

Experiments were performed in vitro with 21 – 26 days old Wistar rats. All experiments in this study were carefully carried out in accordance with the "Principles of laboratory animal care" (NIH publication No. 86-23) as well as with the European Communities Council Directive 86/609/EEC and were approved by the Animal Care and Use Committee of the State Food and Veterinary Service of Lithuania (No 0167). The rats were anesthetized using anesthetic suprane and decapitated. Brain was taken out and kept for a few minutes in an icy cold dissection solution and then moved to the slicing bath filled with the oxygenated icy cold dissection solution. The 400 µm thick slices of cerebellum were made and transferred into the storing chamber where they were kept in the oxygenated extracellular solution at room temperature. The composition of the solutions used was as follows – dissection solution: KCl 1.25 mM, CaCl2 0.5 mM, MgCl2 7 mM, NaHCO3 25 mM, KH2PO4 1.25 mM, glucose 16 mM, glycerol 250 mM; extracellular (perfusion) solution: NaCl 125 mM, KCl 1.25 mM, CaCl2 2 mM, MgCl2 1 mM, NaHCO3 25 mM, KH2PO4 1.25 mM, glucose 16 mM; intracellular solution: K-gluconate 120 mM, KCl 18 mM, MgCl2 2 mM, NaCl 2 mM, Na2ATP 2 mM, HEPES 10 mM.

Whole-cell patch clamp recordings of antidromically evoked action currents were achieved from 13 (10 rats) cerebellar granule cells. Schematic of the experiment is shown in Figure (3).

Figure (3). Schematic of the experiment.

S – stimulation pipette, R – recording patch pipette, PFL – parallel fiber layer, PCL – Purkinje cell layer, GCL – granule cell layer.

Stimulating pipette, filled with the extracellular solution and having resistance ~1.5 MΩ, was placed in parallel fiber layer of the cerebellum. The distance between the stimulating electrode and recording patch pipette was ~1 µm. Voltage pulses of the amplitude of 20–60 V and duration of 50 µs were applied

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through the stimulation electrode using the npi stimulator ISO-STIM 01M. Antidromicaly propagated action currents were recorded in the soma of the granule cells trough the 8 MΩ whole-cell patch pipette using the npi single electrode switching VC, CC amplifier SEC-10LX. Recordings were done in voltage clamp mode at holding membrane potential of -60 mV.

All recordings were done at room temperature ~24 oC and with synaptic blockers 1 mM of KYNA, 20 µM of CNQX and 25 µM of picrotoxin in the perfusion solution. The chemicals were purchased from Sigma-Aldrich Co.

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11. RESULTS

Antidromically propagated axonal (parallel–ascending fiber) action currents have been recorded from 13 cerebellar granule cells of 10 frogs. The figure (4) shows representative recordings from the two granule cells.

Figure (4). Axonal action currents recorded in the two cerebellar granule cells. Art – stimulus artifact, AC – action current, recorded in the cerebellar cell’s soma.

The data of the individual experiments and their averages are listed in the table (1).

No Age, days Response

latency, ms action current, pA Amplitude of the Duration of the action current, ms

1 24 3.06 -382 0.66 2 26 2.02 -325 0.65 3 25 2.32 -380 0.58 4 25 4.3 -104 0.66 5 17 2.66 -412 0.76 6 17 2.18 -257 0.92 7 21 7.44 -204 0.58 8 26 2.39 -379 0.7 9 26 3.69 -311 0.64 10 21 3.96 -293 0.7 11 23 1.71 -288 0.95 12 22 3.48 -193 0.95 13 23 6.28 -625 0.66 Aver 22.8 3.5 -319 0.72 SE 0.9 0.47 35 0.04

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The results of the experiments have demonstrated that the average amplitude, A, and duration, ts, of the

axonal action current recorded in the granule cell soma are equal to -319 ± 35 pA and 0.72 ± 0.04 ms, respectively.

The average latency of the response of 3.5 ms shows that the site of the stimulation of parallel fiber by the stimulating electrode was on average at the distance of 0.8 mm from the granule cell soma (distance = latency × velocity = 3.5 ms × 0.22 m/s = 0.77 mm).

The experiments have been done at room temperature, 24 oC. The rate of the opening/closing of the channels increases with the increase of the temperature. Therefore, duration of the action current at 36o C will be less than at 24o C. Value of the temperature coefficient Q10 for most of biological processes is

equal to 2. Thus, ts(36 oC) = ts(24 oC)/2.297 = 0.31 ± 0.01 ms.

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12. DISCUSION

The results of the experiment can be used for evaluation of the increase of sodium concentration in the cerebellar granule cell axon due to generation of the spike. We use theoretical result from the last year master thesis “Na+ koncentracijos pokyčių nemielinizuotose nervinėse skaidulose teorinis modeliavimas”, Mantas Žibas, 2017 m. The theoretical considerations of the latter work led to the equation:

_∫

⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − + − ⋅ ⋅ − ⋅ − ⋅ ⋅ ⋅ ⋅ ⋅ = s t t a t a x s s e da a t r e A t x c s s 0 4 2 2 / 3 2 2 1 2 ) , ( τ τ λ τ λ π , (1)

where c(x, ts) is an increase of the sodium concentration at the distance x from the site of generation of the

action potential when the action current ends. A is amplitude of the action current, ts – duration of the

action current, r – radius of the axon, τ – time constant of the axonal membrane, λ – length constant of the axon.

The radius of the parallel/ascending fiber is equal to 0.15 µm [35; 72; 93]. Using the standard values for the cytoplasm (axoplasm) resistivity r = 100 Ω⋅cm, membrane specific resistance Rm = 50000 Ω⋅cm2, and

capacitance Cm = 1 µF/cm2 (see, for example, [36]), the τ = 50 ms, λ = 612 µm.

The equation (1) lets us to calculate the distribution of the increase of sodium concentration along the cylindrical axon, caused by the action potential, when the amplitude and duration of the action current are known. Substituting experimentally measured values of the action current amplitude, A, and duration, ts,

into equation (1) gives c(0, ts) = 0.174 ± 0.019 mM. This value is much smaller than the background level

of sodium ion concentration in the cytoplasm of the cerebellar granule cells that is equal to 8 mM [22]. Action currents were recorded in the granule cell somas, i. e. at some distance from the axon initial segment (axon hillock), where the action potentials are initiated. The initial segment of the ascending axon starts within the distance of 10 µm from the soma and stretches 20-40 µm long [12; 22; 35]. Therefore, the somatically recorded currents may be a bit smaller than the currents generated in the initial segment, due to not perfect voltage clamp. Thus, the above calculations give the lower limit for the increase of the sodium concentration in the axon, c(0, ts) ≥ 0.174 ± 0.019 mM.

The above calculations do not account for the sodium ion removal by the Na+/K+ ATP pump. However, the rate of increase of the sodium concentration in the axon during the action potential, ~1000 s-1, is much

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higher than the rate of sodium removal by the pump ~100 s-1 [7; 56]. Thus, within the time of the concentration increase Na+/K+ pumps do not activate appreciably.

Sensory input to the cerebellar granule cells from mossy fibers, generally, elicits bursts of five action potentials with interpulse intervals of ~3 ms [78]. Increase of the sodium concentration in the parallel/ascending fibers of the granule cell axon at the end of the burst will be equal to 0.244 mM, as calculated with the equation (1). Not large differences from the concentration increase 0.174 mM at the peak of a single spike. Even a train of 100 spikes of 500 Hz frequency (interpulse intervals of 2 ms) will not lead to a much larger increase of the sodium concentration. Namely, the increase of the sodium concentration at the end of the train of 100 spikes, calculated using the equation (1), will be equal to 0.439 mM. Only 2.5 times larger than the increase at the end of a single spike. Actually, it will be smaller due to the activity of Na+/K+ ATP pump during the train of the 100 spikes that, in this case, should be accounted for.

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13. CONCLUSION

1. Whole-cell voltage clamp recordings of antidromically evoked action currents in cerebellar granule cells yielded the amplitude and duration of these currents equal to -319 ± 35 pA and 0.72 ± 0.04 ms. 2. On the ground of these results, the lower limit of increase of the sodium concentration in the cerebellar ascending/parallel fibers during the action potential has been evaluated equal to 0.174 ± 0.019 mM. 3. Despite the very small diameter of the ascending/parallel fibers, the increase of the sodium concentration due to the propagation of a single action potential and burst of action potentials is much smaller than the background level of the sodium concentration.

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