SELF-PROPAGATING, NON-SYNAPTIC HIPPOCAMPAL WAVES RECRUIT
NEURONS BY ELECTRIC FIELD COUPLING
By
RAJAT SHAMACHAR SHIVACHARAN
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Thesis Advisor: Dominique M. Durand, PhD
Department of Biomedical Engineering
CASE WESTERN RESERVE UNIVERSITY
May 2019 CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis dissertation of
Rajat Shamachar Shivacharan
candidate for the degree of Doctor of Philosophy*.
Committee Chair
Jeffrey R. Capadona
Thesis Advisor/Committee Member
Dominque M. Durand
Committee Member
Cameron C. McIntyre
Committee Member
Hillel J. Chiel
Date of Defense:
April 8th, 2019
*We also certify that written approval has been obtained for any proprietary material
contained therein. Dedication
To my great grandfathers, Mr. Doddappa Acharya and Mr. Shilipi Shamachar; to my grandparents Mr. Y.S. Shamachar & Mrs. Lalitha, and Mr. H.D. Ramakrishna Sastry & Justice
B.S. Indrakala; for being exemplary role models for me, and for being the luminaries of my
family.
To my Mom & Dad, my brother Manju, our loving, four-legged pup Rocky, and the rest of my
family and friends near and far; for your unwavering love and support throughout my
adventures. Table of Contents
Contents
Table of Contents ...... i
List of Figures ...... vii
List of Tables ...... x
Acknowledgments ...... xi
List of Abbreviations ...... xiv
Abstract ...... xvi
Overview ...... 18
Chapter 1: Introduction and Thesis Organization ...... 21
1.1 Brain Wave Propagation ...... 22
1.2 Hippocampus ...... 23
1.3 Pathological Waves – Epilepsy ...... 24
1.4 Physiological Waves – Slow Oscillation Sleep Waves ...... 26
1.5 Mechanisms of Neural Propagation ...... 27
1.6 Ephaptic, or Electric Field, Coupling ...... 29
1.7 Thesis Organization: Specific Objectives Overview and Hypothesis ...... 30
1.7.1 - Objective 1: To determine if epileptiform waves self-propagate in the hippocampus by electric field coupling...... 31
i
1.7.2 - Objective 2: To determine if spontaneous waves can recruit neurons via electric fields across a physical cut...... 32
1.7.3 - Objective 3: To determine if hippocampal waves under physiological conditions can self-propagate, non-synaptically by electric field coupling...... 32
1.8 Figures...... 34
Chapter 2: Self-propagating epileptiform activity recruits neurons by endogenous electric fields ...... 37
2.1 Abstract ...... 38
2.2 Introduction ...... 39
2.3 Material and Methods ...... 42
2.3.1 Longitudinal hippocampal slice preparation ...... 42
2.3.2 Solution preparation to elicit spontaneous epileptiform activity ...... 42
2.3.3 Electrophysiology recording setup ...... 43
2.3.4 Optical recording setup ...... 44
2.3.5 In vitro osmolarity to study the effect of cell distance on propagation speeds under 4-
AP conditions ...... 44
2.3.6 Extracellular electric field clamp ...... 45
2.3.7 Isopotential experiment setup ...... 46
2.3.8 Data and statistical analysis ...... 46
2.4 Results ...... 47
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2.4.1 4-AP-induced activity propagates along the longitudinal direction of the hippocampus ...... 47
2.4.2 Modifying the extracellular space changes propagation speed of 4-AP-induced activity in vitro ...... 48
2.4.3 Canceling the endogenous electric field with an extracellular electric field clamp blocks propagation of epileptiform activity ...... 49
2.4.4 Increasing the conductivity along the cell layer decreases the magnitude and propagation speed of epileptiform activity ...... 51
2.4.5 Applied electric fields can trigger self-propagating waves in the longitudinal hippocampal slice...... 52
2.5 Discussion ...... 54
2.6 Figures...... 59
Chapter 3: Epileptiform waves propagate through a physical cut solely by self- sustaining electric fields ...... 69
3.1 Abstract ...... 70
3.2 Introduction ...... 71
3.3 Materials and Methods ...... 74
3.3.1 Acute in vivo transection and recording experimental design ...... 74
3.3.2 Longitudinal hippocampal slice preparation ...... 75
3.3.3 Electrophysiology recording setup in vitro ...... 76
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3.3.4 Optical recording setup and image processing ...... 77
3.3.5 Statistical analysis ...... 78
3.4 Results ...... 79
3.4.1 Seizure-like activity propagates through a physical hippocampal transection in vivo acutely ...... 79
3.4.2 Spontaneous epileptiform activity propagates non-synaptically through a cut in vitro.
...... 80
3.4.3 Spatio-temporal dynamics of the epileptiform remain unchanged through a cut in the hippocampus in vitro...... 81
3.4.4 Endogenous electric field can cross a cut and are self-sustaining activity in vitro ...81
3.5 Discussion ...... 83
3.6 Figures...... 87
Chapter 4: Slow oscillation sleep waves can self-propagate non-synaptically by a mechanism consistent with ephaptic coupling ...... 95
4.1 Abstract ...... 96
4.2 Introduction ...... 97
4.3 Materials and Methods ...... 99
4.3.1 Ethical approval ...... 99
4.3.2 Origin and source of the animals ...... 99
4.3.3 In vitro hippocampal slice preparation and recording ...... 99
iv
4.3.4 Optical recordings ...... 101
4.3.5 Statistical analysis ...... 102
4.4 Results ...... 103
4.4.1 Slow hippocampal periodic activity can propagate non-synaptically in the longitudinal hippocampal preparation ...... 103
4.4.2 Slow hippocampal periodic activity can activate neural tissue through a complete gap in the tissue ...... 104
4.4.3 Propagation of the slow hippocampal periodic activity requires dendritic activation ...... 105
4.4.4 Dendritic NMDA spikes are involved in the generation of the slow hippocampal periodic activity ...... 106
4.4.5 NMDA channels are involved in the propagation of the slow hippocampal periodic activity...... 108
4.4.6 Propagation of the slow hippocampal periodic activity can be influenced by increasing the extracellular space ...... 109
4.4.7 Slow hippocampal periodic activity can be simulated in silico by a hippocampal network model connected only with ephaptic coupling ...... 110
4.4.8 Slow hippocampal periodic activity can be modulated by an applied electric field in the extracellular space in silico ...... 112
4.4.9 Propagation of the slow hippocampal periodic activity can be blocked by EEFC in vitro ...... 113 v
4.5 Discussion ...... 114
4.6 Figures...... 120
Chapter 5: Summary and Future Directions ...... 136
5.1 Summary ...... 137
5.1.1 Objective 1: To determine if epileptiform waves self-propagate in the hippocampus by electric field coupling...... 137
5.1.2 Objective 2: To determine if spontaneous waves can recruit neurons via electric fields across a physical cut...... 140
5.1.3 Objective 3: To determine if hippocampal waves under physiological conditions can self-propagate, non-synaptically by electric field coupling...... 141
5.2 Significance...... 143
5.3 Future Directions ...... 144
Appendix ...... 147
A1. Computational Model of Electric Field Coupled Hippocampal Network developed by
Xile Wei, PhD (Professor of Electrical Engineering and Computer Science, Tianjin
University, China) ...... 148
A1. Figures and Tables ...... 154
A2. A 3D printed 2-compartment electrically isolated in vitro slice chamber design and preliminary results completely blocking hippocampal wave propagation across a cut. . 157
Bibliography ...... 159
vi
List of Figures
Figure 1.1: Anatomy of Rodent Hippocampus ...... 34
Figure 1.2: Non-synaptic caffeine induced wave propagation in cerebral cortex ...... 35
Figure 1.3: Ephaptic, or Electric Field, Coupling Mechanism ...... 36
Figure 2.1: Spontaneous epileptiform activity propagating in the longitudinal hippocampal slice preparation ...... 60
Figure 2.2: Modifying extracellular space changes 4-AP propagation speed ...... 61
Figure 2.3: Derivation of extracellular electric field clamp circuit ...... 62
Figure 2.4: Benchtop testing of extracellular electric field clamp ...... 63
Figure 2.5: Extracellular electric field clamp in vitro ...... 64
Figure 2.6: High conductance arrays decrease speed of propagation ...... 66
Figure 2.7: Applying an electric field of similar endogenous amplitude induces a propagating neural wave ...... 67
Figure 2.8: Electric field coupling mechanism ...... 68
Figure 3.1: Acute in-vivo spontaneous epileptiform activity in the hippocampus recording and transection/cut experimental design ...... 87
Figure 3.2: Epileptiform activity propagates through a transection in-vivo acutely ...... 89
Figure 3.3: Epileptiform activity propagates through a cut in-vitro ...... 91
Figure 3.4: Spatio-temporal dynamics of 4-AP activity crossing a cut in-vitro ...... 93
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Figure 3.5: Electric field measurements of epileptiform activity crossing the cut in vitro ...... 94
Figure 4.1: Slow hippocampal periodic activity propagation in vitro ...... 120
Figure 4.2: Slow hippocampal periodic activity can propagate without synaptic transmission ...... 121
Figure 4.3: Slow periodic activity propagation along the tissue with a complete cut in vitro
...... 123
Figure 4.4: Transmembrane voltage imaging and the spatial-temporal features of the slow hippocampal periodic activity ...... 124
Figure 4.5: Slow periodic activity dependent on NMDA and intracellular calcium ...... 125
Figure 4.6: Effects of CNQX, PTX, and Mefloquine on slow periodic activity ...... 127
Figure 4.7: Effect of local APV/NMDA application on slow periodic activity in vitro ..128
Figure 4.8: Effect of modifying extracellular space on slow periodic activity in vitro ...129
Figure 4.9: Slow periodic activity propagating by electric field coupling in silico ...... 130
Figure 4.10: Slow periodic activity propagation can be blocked by an anti-field in silico ...... 132
Figure 4.11: Slow periodic activity propagation can be antagonized or stimulated by electric fields in vitro ...... 135
Figure A1.1: Model of Hippocampal Network ...... 15454
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Figure A2.1: Design and implementation of 3D printed 2-compartment electrically isolated in vitro slice chamber ...... 15757
Figure A2.2: Blocking spontaneous epileptiform wave through a cut ...... 15858
ix
List of Tables
Table A1.1: Parameters under conditions with 3 different calcium concentrations ....15656
Table A1.2: Circuit parameters in computational model ...... 15656
Table A1.3: Hodgkin-Huxley equations of different channels in the model ...... 15656
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Acknowledgments
This work would not have been possible without the help and support of others to whom I am extremely appreciative.
I would like to thank my advisor, Dr. Dominique Durand, for his support and guidance in my research and for showing me how to think critically, formulate experimental and practical hypotheses while carrying out complex science. You took me on with no experience in brain electrophysiology and helped me grow with confidence as an independent scientist and engineer to accomplish everything I have done for the past six years. You helped mold me in the research scientist I am today, and for that I am extremely grateful.
Thank you to my committee members, Dr. Jeffrey Capadona, Dr. Hillel Chiel, and
Dr. Cameron McIntyre for their expert advice and guidance throughout my graduate studies. I would also like to thank Dr. Luis Gonzalez-Reyes, Dr. Mingming Zhang, and Dr.
Chia-Chu Chiang for not only being invaluable mentors throughout the different points of my graduate career, but for the insightful discussions and debates inside and outside of lab.
I thank the members of the Durand Lab, past and present: Chen Qiu, Thomas Ladas,
Luis Gonzalez-Reyes, Yazan Dweiri, Mingming Zhang, Thomas Eggers, Xile Wei,
Xiaohong Sui, Arvind K. Ananthakrishnan, Chia-Chu Chiang, Grant McCallum, Bill
Marcus, Yi-Jen Wu, Nicholas Couturier, Muthumeenakshi Subramanian, Joseph
Marmerstein, Jay Shiralkar, Nrupen Pakalapati, Rachael Matthew, and Yasmine Wazni.
None of the work presented here would have been possible without your support. There are no words to express how grateful I am for getting to know all of you inside and outside
xi
of lab. I have grown personally as an academic, a researcher, and mentor because of you, and you made carrying out research everyday for the past 6 years exciting! “Durand’s Lab
– Where Miracles Happen!”
To my friends and professors in the Neural Engineering Center and Functional
Electrical Stimulation Center, past and present, thank you for all the support and friendship that kept me grounded while I pursued my doctoral degree. You helped expand my knowledge of the ever-growing field of neural engineering and neuromodulation. A special thanks to Natalie Cole and Daniel Young for keeping me on my toes and entertained while working at my desk.
I would like to thank my Mom and Dad, my brother Manju, my adorable dog
Rocky, and to the rest of my family, who stood by me while I searched and found my passion. All the values and life moments we shared have helped shaped me into the individual I am today.
Finally, I came to Cleveland knowing no one, but in my 6 years here at Case
Western Reserve University, I have come to know and adore many people that I consider to be my closest friends. From friends I made throughout my graduate career to friends I made outside of school, all of you have had a significant impact on my life as I navigated the treacherous graduate school climb. Thanks to everyone in the Wolfpack family, including Nadia Ayat, Peter Bielecki, Nate Braman, Natalie Cole, Danielle Conneely, Gil
Covarrubias, Christopher Hernandez, DaShawn Hickman, Selva Jeganathan, Nick
VanDillen, Brian Widman, and Alice Yang. I will cherish all the memorable memories we had during my time in Cleveland and I hope we can create many more.
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A special thanks to Nadia Ayat, Natalie Cole, Christopher Hernandez, and Alice
Yang for being my OG family from day one and for always being there for me. Without the adventure, the laughter, and just good old chilling after a long day of research, I wouldn’t have made it to this point without you. I hope I can have the same impact on your life as you have had on mine as we all take the next leap in our careers. #FriendsForLife
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List of Abbreviations 4-AP 4-aminopyridine
NMDA N-methyl-D-aspartate
APV 2-amino-5-phosphonopentanoic acid
EEG Electroencephalogram
ENG Electronystagmography
ECoG Electrocorticography
REM Rapid eye movement
DBS Deep brain stimulation
LFP Local field potential
LTP Long-term potentiation
MTLE Mesial temporal lobe epilepsy tDCS Transcranial direct current stimulation tACS Transcranial alternating current stimulation
TMS Transcranial magnetic stimulation aCSF Artificial cerebrospinal fluid
VSFP Voltage sensitive fluorescent proteins
GEVI Genetically encoded voltage indicators
LED Light emitting diode
CMOS Complementary metal-oxide semiconductor
CD-1 Crl:CD1(ICR) mouse
DG Dentate gyrus
CA3 Cornu ammonis 3
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CA1 Cornu ammonis 1
CD-1 Crl:CD1(ICR) mouse mV/mm Millivolt per millimeter m/sec Meter per second mm Millimeter msec Millisecond sec Second
Hz Hertz kHz Kilohertz mM Millimolar
µM Micromolar
µL Microliter
IACUC Institutional Animal Care and Use Committee
NIH National Institute of Health
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Self-propagating, Non-synaptic Hippocampal Waves Recruit Neurons by Electric Field
Coupling
Abstract
By
RAJAT SHAMACHAR SHIVACHARAN
It is well documented that synapses play a significant role in the transmission of information between neurons. However, in the absence of synaptic transmission, neural activity has been observed to continue to propagate. This raises the question as to what is mediating this propagation. Previous experiments in our lab have shown that spontaneous epileptiform waves in rodent hippocampi propagates at a speed of ~0.1 m/sec. This observed propagation can take place in the absence of synaptic transmission and gap junctions, and its speed does not correspond to that of ionic diffusion or axonal conduction.
Computer simulations indicate that ephaptic coupling, or electric fields, could be responsible for this propagation of neural activity in pathological conditions such as epilepsy. However, there is no experimental data suggesting ephaptic coupling is a critical mechanism for spontaneous, self-regenerating propagation of neural activity. Using in vitro and in vivo experiments complemented by computational modeling, we test the hypothesis that ephaptic coupling is a critical mechanism for self-propagating, non-synaptic hippocampal wave propagation. We first show that spontaneous epileptiform waves self- propagate by endogenous electric field by carrying out a series of experiments that modify the extracellular space and the endogenous field. Second, we show that spontaneous waves
xvi
are non-synaptic, self-propagating waves mediated by ephaptic field coupling by showing that epileptiform waves can propagate through a complete physical cut of the tissue, therefore, eliminating all other forms of close cell-to-cell communication and showing that electric fields alone are sufficient to mediate non-synaptic propagation. Finally, we show that electric fields can explain not only pathological waves traveling in the brain but can also explain travelling physiological waves such as slow oscillation sleep waves. The findings from this study lay the foundation of the role of electric field coupling as a non- synaptic mechanism in the brain that could have significant importance on brain wave under both pathological and physiological conditions.
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Overview
Understanding how neurons communicate with one another is vital for understanding how information is transmitted throughout - a necessary basic function for life. It is well documented that synapses play a significant role in transmitting information between neurons. However, in the absence of synaptic transmission, neural waves under both pathological and physiological conditions are observed traveling throughout the brain.
Thought to be reflections of underlying neural activity, it is unclear what mechanism is driving these brain waves. Another question is whether or not these fields can play an active role in neural activity by exciting neural populations in regions of the brain such as the hippocampus. The goal of the dissertation work is to answer these questions by determining if a non-synaptic mechanism such as ephaptic, or electric field, coupling can allow neural waves to self-propagate in the hippocampus. The dissertation is organized in the following five chapters.
Chapter 1: Introduction and Thesis Organization
This chapter provides a background into what brain waves are and describes the mechanism of how neurons communicate with one another. In addition, examples of pathological and physiological waves are described with a rationale for why these examples were the focus of this dissertation. Finally, we describe how brain waves, regardless of experimental model, propagate at a unique speed of 0.1 m/sec. This section includes the objectives and hypotheses of this dissertation.
Chapter 2: Self-propagating epileptiform activity recruits neurons by endogenous electric fields
18
Spontaneous epileptiform waves induced by 4-AP, an epileptogenic agent, have been observed to travel in the hippocampus at 0.1 m/sec. Previous computer simulations suggest that electric fields are involved in 0.1 m/sec activity. In this chapter, we investigate if spontaneous epileptiform waves can self-propagate by electric field coupling. Using in vitro electrophysiology techniques and novel experiments, we present concrete experimental evidence showing electric fields playing a significant role in recruiting neurons and generating self-propagating epileptiform activity.
Chapter 3: Epileptiform waves propagate through a physical cut solely by self- sustaining neuro-electric fields
Electric fields can propagate through volume conductors. In this chapter, we investigate if spontaneous epileptiform waves can travel through a physical cut, thereby eliminating all forms of synaptic transmission and other cell-to-cell mechanisms. Using acute in vivo and in vitro electrophysiology techniques and computer modeling, we study the cellular and system level mechanism of self-sustaining electric fields driving spontaneous waves in the hippocampal network.
Chapter 4: Slow oscillation sleep waves can self-propagate non-synaptically by a mechanism consistent with ephaptic coupling
Understanding the functional role of electric field coupling is of upmost importance as it may explain mechanisms of brain functions such as memory consolidation. With physiological waves such as theta and slow-oscillation sleep waves propagating at 0.1 m/sec in the brain, it is important to study electric field coupling under physiological conditions to determine if they are relevant in these conditions. In this chapter, we determine if slow oscillation sleep waves self-propagate non-synaptically by electric field 19
coupling. We characterize these sleep waves traveling in the hippocampus and use computer modeling and in vitro experiments to study the role of electric fields under these physiological conditions.
Chapter 5: Summary and Future Directions
This chapter serves to summarize the results, and their interpretation, found within this dissertation. Additionally, the significance of this work to the neural engineering and neuroscience community is discussed. Finally, a discussion of future directions and alternative experiments with preliminary data are also included.
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Chapter 1: Introduction and Thesis Organization
21
1.1 Brain Wave Propagation
Brain waves are produced by a population of neurons communicating with one another. These waves can travel within and between different regions of the brain and this form of communication is important for transmitting neural information or synchronizing neural networks (1–6). These propagating periodic waves are detected in the brain as oscillations and have been observed to propagate in humans, non-human primates, and other mammals including rodents (7–11). The oscillatory waves capture the dynamics of neural networks or neuronal populations that are essential for both normal brain function as well as for neural disorders like epilepsy (12–17). These waves have been associated with common physiological functions including memory consolidation, emotional processing, spatial navigation, and motor movement commands (7, 8, 18–23).
These waves can be characterized by their spiking frequency or amplitude (i.e. delta, theta, gamma, etc.) or by their spiking patterns (bursting, sharp-wave, slow-wave, high oscillation ripples, etc.), or their spatiotemporal properties (NMDA spike, Ca2+ spike, direction of propagation) (12, 24–38) and can be monitored by EEG, ENG, ECoG, single or multi-channel depth electrodes, or high density microelectrode arrays. Several studies with animal models or human subjects have described different patterns of these traveling brain waves with little understanding of the mechanism behind them (7, 10, 17, 38–40).
Brain waves are considered reflections of underlying neural activity and thought to be a summation of multiple, synchronized neurons’ local field potentials (LFP). Propagating waves in the hippocampus are of particular interest not only for their unique anatomy but also for their patho-physiological functional role in the brain. However, it is undetermined
22
if these waves can excite neurons and self-propagate, which is the overarching goal of this thesis dissertation.
1.2 Hippocampus
The hippocampus, located in the temporal lobe of the brain, is at the center of the limbic system that includes the hypothalamus, anterior thalamus, cingulate cortex, and amygdala. The pyramidal neurons of the hippocampus are tightly packed to form a distinctive laminar structure. The hippocampus contains two types of orthogonal circuits: the transverse lamellae that is made of the tri-synaptic pathway and the longitudinal pathway that runs along the longitudinal axis (temporal to septal pole) of the hippocampus
(Fig. 1.1A) (41, 42). The transverse lamellae are organized in parallel loops that originate and end in the entorhinal cortex. The hippocampus has four sub-regions that form a tri- synaptic pathway, consisting of the dentate gyrus (DG), Cornu Ammonis regio superior
(CA1), Cornu Ammonis regio inferior (CA3), and the subiculum. These regions are connected as follows: the DG projects to principal pyramidal neurons in the CA3 regions via mossy fiber axons; CA3 neurons project to CA1 pyramidal neurons via Schaffer collateral axon fibers; CA1 neurons projects to the subiculum. Neurons in the CA3 regions form excitatory synapses on neighboring CA3 neurons. From the hippocampus, there are projections to and from other structures of the limbic systems and cortex, creating a feedback loop (43) . These projections and the above-mentioned tri-synaptic pathway are demonstrated in the rat hippocampus in Fig. 1.1B (44, 45).
There have been decades of research looking into the functional significance of the hippocampus. Two important functions that hold true today that have been studied in the 23
transverse tri-synaptic pathway are memory processing/recall and spatial cognition (46–
53). The longitudinal pathway has been found to be important for neuronal synchronization or generation of epileptic seizures (14, 15, 23, 49, 54–56). Furthermore, it has been shown that generalized cortical seizures arise from propagation of spontaneous epileptiform activity along the longitudinal pathway (Fig. 1.1C) in the hippocampus (25, 57). Mesial temporal lobe epilepsy (MTLE) is the most common and medically refractory form of epilepsy and the hippocampus is the common location of the development and progression of MTLE (54, 57–59).
1.3 Pathological Waves – Epilepsy
Epilepsy is the most common neurological disorder that is characterized by an enduring predisposition to generate epileptic seizures. Epilepsy affects the whole age range from neonates to the elderly, and is a complex disease with varied causes and manifestations resulting in abnormal electrical activity within the brain (60). According to the Centers for Disease Control and Prevention, in 2015, 1.2%, or 3.4 million people, of the US population suffer from active (doctor-diagnosed) epilepsy (61). In an epileptic brain, the abnormal electrical activity can create symptoms of generalized or partial seizures. There are at least two distinct pathological waveforms in an epileptic brain: ictal
(seizure) activity and interictal activity (low frequency spiking/waves between seizures)
(62, 63). Each of these events are hard to predict as they can occur randomly in the diseased brain. To study epilepsy, there are models that can only reproduce certain biomarkers of epilepsy. We define ictal activity as periodic, high frequency oscillations/spiking of at least
10 Hz lasting a minimum duration of one to two seconds. Interictal activity is defined as
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spontaneous epileptiform activity consisting of single or burst of spikes/waves lasting a maximum of 100-150 milliseconds, occurring between seizures that are often high amplitude and range from 0.2 Hz to 3 Hz. It has been reported that there are two components of neural propagation in spontaneous epileptiform activity: fast propagating spikes, and slow propagating waves (10, 17, 28, 34).
The mechanism of how epileptiform activity is generated and recruits neurons is widely controversial with many theories present in literature (2, 10, 12, 64–66). Recently, we have provided strong experimental evidence for a non-synaptic mechanism that can explain how epileptiform activity recruits neurons and propagates through the brain, which
I will describe in Chapters 2 and 3 (Aim 1 and 2).
In the field of neuroscience, animal models are used to study complex questions for understanding how the human brain works. There are three conditions under which one can study neural propagation in animal models: spontaneous endogenous neural activity, pharmacologically induced activity, and activity induced by electrical or optical stimulation. Spontaneous epileptiform activity can be induced pharmacologically with 4-
Aminopyridine (4-AP) or kainic acid, or optically in optogenetic mice carrying voltage fluorescence sensitive proteins (35, 56). To study how epileptiform waves recruit neurons and propagate in the brain, I studied 4-AP-induced spontaneous epileptiform activity traveling in the rodent hippocampus. 4-AP is an epileptogenic agent that blocks Kv1 voltage-activated K+ channels to generate hyper-excitable neural tissue/networks and is often used to induce epileptiform activity in the brain (35, 67). 4-AP-induced epileptiform activity is N-methyl-D-aspartate (NMDA) sensitive making it an ideal epilepsy model to
25
study in the hippocampus where NMDA receptors are abundant for synaptic plasticity and memory consolidation (34–36, 52, 68–73).
1.4 Physiological Waves – Slow Oscillation Sleep Waves
Endogenous neural waves in a normal brain are characterized as slow oscillation electrical activity. Throughout a given day, the brain uses different waves to process certain situations. These physiological waves can be characterized by five frequency-dependent categories: delta (0-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), beta (12-40 Hz), and gamma
(40-100 Hz). Within each of these frequency bands, researchers have categorized various brain states and functions. Most recently, gamma waves have been implicated in the unity of conscious, the idea that different regions of the brain are stimulated simultaneously
(neurons oscillate in synchrony even though they are not directly connected) and have been observed in the visual cortex (74–77). Beta waves are often associated in awake brains with active movement, cognitive reasoning, speaking or thinking (8, 78–80). Alpha waves, centered in the occipital lobe, are thought to be the bridge between conscious thinking
(beta) and the subconscious (theta) (i.e. wakeful sleep, closed eyes). Recent studies suggest alpha waves inhibit areas of the cortex not in use, or otherwise play a role in network coordination (81). Theta waves, detected predominantly in the hippocampus and other cortical/subcortical brain structures, are observed during exploratory motor behaviors, rapid eye movement (REM) sleep, and are thought to be associated with memory consolidation (7, 19, 39, 75, 82). Finally, delta waves are associated with deep sleep, or slow-wave sleep and are the slowest brainwaves detectable by EEG.
26
It has been observed that physiological waves like beta, theta, and delta waves travel in the brain, but the mechanism of how they propagate is unclear. In Chapter 4 (Aim
3), we investigate the mechanism of slow oscillation sleep waves (<1 Hz) traveling in the hippocampus. These sleep waves were reproduced in in vitro hippocampal slices from an in vitro cortical slice preparation that mimicked in vivo slow oscillations (38).
1.5 Mechanisms of Neural Propagation
Interestingly, some neural spikes and waves propagate at speeds of ~0.1 m/sec regardless of experimental models (Fig. 1.1D). Neural activity generated by 4-AP in the
CA3 travels longitudinally at a speed of 0.09 ± 0.03 m/sec (14). In the presence of picrotoxin, events propagate longitudinally at 0.14 ± 0.04 m/sec (15). Epileptiform behavior induced by high K+ aCSF, low Mg2+ aCSF, and non-synaptic low Ca2+ aCSF produced propagating speeds of 0.07 - 0.15 m/sec (16), (13), (17). In normal physiological and carbachol-induced conditions, theta oscillations travelled longitudinally in the hippocampus with a speed of 0.09 - 0.14m/sec (7), (18). From these studies, it is clear that
0.1 m/sec is a common propagation speed. Therefore, a shared fundamental mechanism may mediate these events.
There are several mechanisms known to be involved in neuron to neuron communication: synaptic transmission, axonal conduction, gap junction transmission, ionic diffusion, and ephaptic (electric field) transmission.
Chemical synaptic transmission, the most common mechanism in the brain, links the membranes of neighboring neurons together to transmit electrical activity. It is widely
27
known to mediate both excitatory and inhibitory activities in the nervous system. Electrical signals travel down the cell’s axon to the pre-synaptic terminal where neurotransmitters are released into the synaptic cleft. The neurotransmitters then bind to the neighboring cell’s post-synaptic receptors and initiate an electrical response in the post-synaptic cell.
An example where chemical synaptic transmission plays an important role is in the transverse plane of the hippocampus that contains the tri-synaptic pathway. This pathway has been linked to long term potentiation (LTP) in the hippocampus, which explains how the brain stores memory by altering the strength of the synaptic connection between neurons (52, 53, 83). Synaptic transmission and axonal conduction are both required for orthodromic conduction from a pre-synaptic cell to a post-synaptic cell. Pure axonal conduction in the brain propagates at speeds between 0.3 and 0.5 m/sec in various animal models (15, 84). A combination of these two mechanisms lowers this propagation speed due to the synaptic delay.
A second type of neuron-to-neuron communication is electrical synapses, or gap junction transmission. These physical cell-to-cell connections are made of transmembrane protein channels allowing electrical current to flow between neighboring cells (85, 86). In the hippocampus, transmembrane protein connexin-36, which forms gap junctions on the mossy fiber axons between pyramidal cells, has been linked to synchronizing firing within cortical, thalamic, and brainstem circuits (87–89).
A third type of neural communication is mediated by ionic diffusion in the extracellular space. It has been reported that ions can diffuse throughout brain tissues and can affect membrane polarization (90). It has been shown that ionic diffusive coupling can
28
cause seizure-like activity to propagate, but the reported speed is 10 to 100 times slower than axonal conduction and synaptic transmission (17, 90, 91).
Previous experiments in our laboratory have shown that spontaneous epileptiform activity can still travel in the hippocampus at ~0.1 m/sec and is uninterrupted in the presence of presynaptic-blocks such as low Ca2+ aCSF and gap junction blockers such as mefloquine (12). Other propagation mechanisms (ionic diffusion and axonal conduction) have very different propagation speeds. Seizure-like activity caused by the diffusion of the
K+ ions propagates at speeds from 0.0004 to 0.008 m/sec (90–92). Axonal conduction velocity in the hippocampus varies from 0.3 to 0.5 m/sec (14, 15, 84, 93). Therefore, neural activity propagating at approximately 0.1 m/sec is independent of all the above mentioned mechanisms. The only other known mechanism of communication between neurons is ephaptic, or electric field, coupling.
1.6 Ephaptic, or Electric Field, Coupling
Ephaptic coupling was theorized as a mechanism whereby electrical activity generated by nervous tissue may influence the activity of surrounding nervous tissue. In
1940, experiments by Katz and Schmitt demonstrated in the limb nerve of a crab Carcinus maenas that the action potential in one excited non-myelinated nerve could cause excitability changes in the neighboring inactive, non-myelinated nerve (94). In 1941, Ralph
W. Gerard showed that caffeine-induced waves could travel rostro-caudal over the frog cerebral hemisphere non-synaptically at a speed of ~0.05 m/sec and hypothesized that intercellular electrical currents could be the mechanism behind this wave propagation (Fig.
1.2) (95). This coupling mechanism works on a small scale where a group of neurons 29
generate an extracellular electric field in the extracellular space that then depolarizes the neighboring cells (Fig. 1.3). The extracellular field effect has been observed axon-to-axon, cell-to-cell, and in synaptic clefts where Ca2+ channels are influenced by local fields (96–
100).
Ephaptic, or endogenous electric field, coupling has been clearly demonstrated in cortical neurons (97) but is thought to be too weak to mediate self-propagating activity.
However, it could be relevant in the hippocampus due to the highly structured and dense cellular packing. It has been reported that extracellular voltages can be modified by weak electrical fields around the soma and dendrites, and an externally applied electrical field with a similar amplitude could affect pharmacologically evoked hippocampal network activity (101, 102). The electrical field effect also has been shown to synchronize neurons and axons, allowing for specific action potential timing with relatively constant propagation speeds (96, 103). The amplitudes of these fields range between 1 to 7 mV/mm in the brain (103–105). However, none of these studies have shown directly that these electric fields can mediate neural propagation.
1.7 Thesis Organization: Specific Objectives Overview and Hypothesis
Recent experiments in our group have provided empirical and theoretical evidence that endogenous electric fields could indeed be the cause of non-synaptic propagation of epileptiform activity (12, 106). These in vitro experiments and in silico simulations indicate that electric fields may be capable of mediating propagation of self-regenerating neural activity but the mechanism has not yet been established. The primary goal of this dissertation is to provide direct experimental evidence that spontaneous activity 30
propagating at ~0.1 m/sec in the hippocampus is mediated by electric field coupling.
Furthermore, this study explored whether hippocampal waves self-propagate by electric fields and if they are driven by the purely non-synaptic mechanism. Using computer modeling and in vitro/in vivo electrophysiology techniques combined with state-of-the-art imaging of transmembrane voltages using genetically encoded voltage indicators (GEVI), we study this fundamental phenomenon in the following 3 objectives.
1.7.1 - Objective 1: To determine if epileptiform waves self-propagate in the hippocampus by electric field coupling.
Rationale: As stated above, regardless of experimental model, brain waves travel in the hippocampus at ~0.1 m/sec and cannot be explained by traditional mechanisms of neural communication (7, 12–18). Computer modeling has shown that under excitable conditions, such as spontaneous epileptiform behavior, activity can propagate at 0.1 m/sec by electric fields between 2-5 mV/mm (106). However, there is no experimental evidence suggesting this 0.1 m/sec propagating activity is mediated solely by electric field coupling and thus requires further investigation. In Chapter 2, we hypothesized that spontaneous epileptiform waves can self-propagate by ephaptic, or electric field, coupling. Within this chapter, we designed and carried out multiple different in vitro experiments in the longitudinal axis (temporal to septal pole) of the rodent hippocampus where we pharmacologically modified the extracellular space, antagonized the extracellular electric field to control spontaneous epileptiform propagation, and stimulated the electric field to generate spontaneous propagation.
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1.7.2 - Objective 2: To determine if spontaneous waves can recruit neurons via electric fields across a physical cut.
Rationale: Previous studies investigated the role of electric fields in non-synaptic environments by blocking chemically-mediated synaptic transmission (12). Since electric fields propagate through volume conductors, 0.1 m/sec spontaneous activity should propagate through a physical cut thereby eliminating all forms of synaptic transmission and close cell-to-cell mechanisms. In Chapter 3, we hypothesized that by propagating through a physical cut, spontaneous self-propagating epileptiform waves are non- synaptic and purely mediated by electric field coupling. In both computer modeling and in acute in vitro/in vivo experiments, we studied the cellular and system level mechanism of spontaneous epileptiform activity crossing a physical cut.
1.7.3 - Objective 3: To determine if hippocampal waves under physiological conditions can self-propagate, non-synaptically by electric field coupling.
Rationale: Until now, we have investigated electric field coupling as a possible mechanism for how epileptiform waves recruit neurons and travel through the brain. To start to understand the functional relevance of electric field coupling in the brain, we needed to study this mechanism under physiological conditions. It has been observed that theta wave and slow oscillation sleep waves propagate in the brain at approximately 0.1 m/sec (7, 38). However, the mechanism behind these propagating physiological waves is unclear and required further investigation. In Chapter 4, we hypothesized that slow oscillation sleep waves self-propagate, non synaptically by electric field coupling.
Specifically, we test if slow oscillation waves behave similarly to epileptiform waves when 32
traveling through the hippocampal network. To test this hypothesis, we first characterized slow oscillation sleep waves traveling in the hippocampus by applying multiple pharmacological agents and determining if spontaneous slow oscillation waves propagate non-synaptically through a physical cut. Using computer modeling and in vitro experiments designed in Chapter 1 and 2, we investigated if these slow oscillation sleep waves can self-propagate by electric field coupling.
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1.8 Figures
Figure 1.1: Anatomy of Rodent Hippocampus
(A) Illustration of a single rodent hippocampi located in the temporal lobe with the longitudinal axis (temporal-septal pole). Illustration by Tiffany Yang. (B) Illustration of the transverse plane of the rodent hippocampus showing the “tri-synaptic” pathway and connection to and from other regions of the limbic system. Illustration modified from
Santiago Ramon y Cajal (1911). (C) Experimental procedure for making longitudinal hippocampal slices used throughout this dissertation. (D) Example LFP recording showing
4-AP-induced epileptiform waves traveling at ~0.1 m/sec from the temporal to septal pole.
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Figure 1.2: Non-synaptic caffeine induced wave propagation in cerebral cortex
Adapted from R. W. Gerard (1941) (95). (A) B. From a frog brain. a. caffeine wave traveling rostro-caudal along the hemisphere. b. after complete transection of the brain showing non-synaptic propagation across the cut. (B) Schema of cell layer in frog’s cerebral hemisphere. A caffeine wave is spreading as indicate by arrow 3 and just discharged the somatic polarization of cell A. Cell B is discharging. The amplifier shows a pial surface positive wave of 1 mV. The interior-exterior polarization of the neuron surface shown in cell F.
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Figure 1.3: Ephaptic, or Electric Field, Coupling Mechanism
A group of pyramidal cells become excitable and depolarize in the dendritic tree (NMDA- dependent), creating a current sink in the dendrites which results in an extracellular electric field being generated between the soma and dendrites. This field passively depolarizes the neighboring neurons. This cycle repeats in hippocampal network, generating a self- propagating event.
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Chapter 2: Self-propagating epileptiform activity recruits neurons by endogenous
electric fields
Parts modified with permission from Journal of Neuroscience, 2015, Vol. 35, Issue 48, December 2015, pp. 15800-15811; Copyright© Society for Neuroscience Publisher Can Neural Activity Propagate by Endogenous Electrical Field? Chen Qiu, Rajat S. Shivacharan, Mingming Zhang, and Dominique M. Durand
Modified with permission from Experimental Neurology, 2019, Vol. 317, July 2019, pp. 119-128; Copyright© Elsevier Publishing Self-propagating, non-synaptic epileptiform activity recruits neurons by endogenous electric fields Rajat S. Shivacharan*, Chia-Chu Chiang*, Mingming Zhang, Luis E. Gonzalez- Reyes and Dominique M. Durand *These authors contributed equally
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2.1 Abstract
It is well documented that synapses play a significant role in the transmission of information between neurons. However, in the absence of synaptic transmission, neural activity has been observed to continue to propagate. Previous studies have shown that propagation of epileptiform activity takes place in the absence of synaptic transmission and gap junctions and is outside the range of ionic diffusion and axonal conduction. Computer simulations indicate that electric field coupling could be responsible for the propagation of neural activity under pathological conditions such as epilepsy. Electric fields can modulate neuronal membrane voltage, but there is no experimental evidence suggesting that electric field coupling can mediate self-regenerating propagation of neural activity. Here we examine the role of electric field coupling by modifying the extracellular space by changing the osmolarity of the tissue. We show that 4-AP-induced activity generates an electric field capable of activating neurons on the distal side of the cut. Experiments also show that applied electric fields with amplitudes similar to endogenous values can induce propagating waves. Finally, we show that canceling the electrical field at a given point can block spontaneous propagation. The results from these in vitro electrophysiology experiments suggest that electric field coupling is a critical mechanism for non-synaptic neural propagation and therefore could contribute to the propagation of epileptic activity in the brain.
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2.2 Introduction
The hippocampus is a common focus of seizures or epileptiform activity in mesial temporal lobe epilepsy and important for basic neural functions such as memory consolidation or spatial navigation(51, 107, 108). The hippocampal neural circuitry is organized into lamellae, or parallel strips of tissue in the transverse plane connected along the longitudinal direction (41). Although it has been reported that there are synaptic connections both in the transverse and longitudinal directions (42, 49, 109), recent observations show that spontaneous activity can propagate in hippocampus at speed much slower that synaptic/axonal conduction. Neural signals, especially epileptiform activity, can propagate along both the transverse and longitudinal septal-temporal axis of the hippocampus at speeds ~0.1 m/sec in both in vitro models and human patients (12, 42,
110). Spontaneous epileptiform activity generated by 4-Aminopyridine (4-AP) in the CA3 region travels longitudinally at a speed of 0.09 ± 0.03 m/sec (14). In the presence of picrotoxin, activity propagates longitudinally at 0.14 ± 0.04 m/sec (15). Epileptiform behavior induced by high K+ aCSF, low Mg2+ aCSF, and non-synaptic low Ca2+ aCSF generates activity propagating at 0.07 to 0.15 m/sec (13, 16, 17). Under physiological conditions, slow periodic activity or slow wave sleep propagates in the hippocampus and the neocortex with a mean speed around 0.1 m/sec (26, 38). Therefore, 0.1 m/sec is a common propagating speed, and as a result, a non-synaptic fundamental propagation mechanism may underlie many of these events.
Several studies suggest that epileptiform activity can propagate by non-synaptic mechanisms (64, 101). It has been shown that spontaneous epileptiform activity can still
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travel at ~0.1 m/sec in the presence of presynaptic-blockers such as low Ca2+ aCSF and gap junction blockers such as mefloquine (12). Other propagation mechanisms (ionic diffusion and axonal conduction) have very different propagation speeds. Seizure-like activity caused by the diffusion of K+ ions propagate at speeds from 0.0004 to 0.008 m/sec
(90–92). Axonal conduction velocity in the hippocampus varies from 0.3 to 0.5 m/sec (14,
15, 84, 93). Therefore, the observed epileptiform activity propagating at approximately 0.1 m/sec is independent of all the above-mentioned mechanisms. Therefore, electric field coupling, or ephaptic coupling, is the only other mechanism of communication between neurons that could explain these results
Electric field coupling has been observed in cortical neurons, but it is thought to be too weak to mediate self-propagating activity (97). Extracellular voltages can be modulated by weak electrical fields around the soma and dendrites, and externally applied electric fields can affect pharmacologically evoked hippocampal network activity (101, 102, 111,
112). Electric fields have also been shown to synchronize neurons and axons, allowing for specific action potential timing with relatively constant propagation speeds (96, 103).
Recently published studies by our group have provided empirical and theoretical evidence that endogenous electric fields could underlie non-synaptic propagation under both pathological (12, 34, 106) and physiological conditions (26). Furthermore, it has been shown experimentally that 4-AP-induced non-synaptic epileptiform waves are NMDA- dependent and computer simulations support the hypothesis that propagation of NMDA- dependent waves can only propagate by electric field coupling (34). Computer simulation experiments suggest that electric field coupling could explain the non-synaptic
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epileptiform propagation, and predict that osmolarity changes should affect the speed
(106).
Taken together, these observations suggest that NMDA-sensitive extracellular waves induced by 4-AP are self-propagating by electric field coupling. Therefore, the purpose of this study is to determine if electric field coupling is both a necessary and sufficient mechanism to explain the propagation of spontaneous epileptiform activity.
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2.3 Material and Methods
2.3.1 Longitudinal hippocampal slice preparation
Experimental protocols were reviewed and approved by the Institutional Animal
Care and Use Committee (IACUC) at Case Western Reserve University. CD1 mice from
Charles River or VSFP-Butterfly 1.2 transgenic mice (for imaging) from The Jackson
Laboratory of either sex aged P10-P20 were anesthetized using isoflurane. Upon decapitation, the brain was placed in an ice cold (3-4 °C), oxygenated (95% O2, 5% CO2), sucrose enriched artificial cerebral spinal fluid (aCSF) solution. The brain was then sectioned by removing the cerebellum and separating the two hemispheres along the midline. From each hemisphere, the hippocampus was extracted from the temporal lobe of the brain (Fig. 2.1A). Longitudinal slices were made by placing the extracted hippocampi on a-custom made agar gel block, with the hippocampal sulcus facing up, and rotated by
90°. The rotated hippocampus-gel was then glued to the stage of the vibratome (VT1000S,
Leica Microsystems). Another agar gel block was placed on the other side of the hippocampus to stabilize the tissue while slicing. The tissue was sliced in an oxygenated sucrose bath to a thickness of 400 µm and then transferred to a chamber contained oxygenated aCSF. Slices were incubated for at least one-hour post-surgery at room temperature (25 °C) prior to recording.
2.3.2 Solution preparation to elicit spontaneous epileptiform activity
Normal aCSF buffer solution consists of the following (in mM): 124 NaCl, 3.75
KCl, 1.25 KH2PO4, 2 MgSO4, 26 NaHCO3, 10 Dextrose, and 2 CaCl2. Sucrose enriched aCSF buffer solution contains (in mM): 220 Sucrose, 2.95 KCl, 1.3 NaH2PO4, 2 MgSO4, 42
26 NaHCO3, 10 Dextrose, 2 CaCl2. To elicit a spontaneous epileptiform activity from the tissue, 100 µM 4-aminopyridine (4-AP), a Kv1 potassium channel blocker was added to normal aCSF. Low Ca2+ aCSF, commonly used to block synaptic transmission by inhibiting pre-synaptic neurotransmitter release, was made with the following recipe (in mM): 124 NaCl, 5.25 KCl, 1.25 KH2PO4, 1.5 MgSO4, 26 NaHCO3, 10 Dextrose, and 0.2
CaCl2.
2.3.3 Electrophysiology recording setup
An interface perfusion slice chamber (BSC-ZT, Harvard Apparatus) that keeps tissue viable with temperature control and oxygenation was used to conduct the experiments in this study. The longitudinal slice was transferred from the recovery chamber to the interface chamber that has oxygenated and temperature controlled (32-34 °C) normal aCSF solution perfusing over the tissue slice. Glass recording electrodes were made from pulled fire-polished borosilicate glass micropipettes (0.5 mm inner diameter, 1.0 mm outer diameter) filled with 150 mM NaCl solution. An Ag/AgCl wire connected the filled glass recording electrode to an HS-2A head stage with a gain of one (Molecular Devices). The reference electrode for the recording electrodes was placed parallel to the tissue slice in the aCSF solution environment. All signals were amplified using an Axoclamp-2A microelectrode amplifier (Axon Instruments), and low-pass filtered (5 kHz field potentials) with additional amplification (FLA-01, Cygnus Technology). The signal is then digitized at 40 kHz by a recording data acquisition unit (PowerLab, AD Instruments), and stored in a computer for further analysis. The direction of spontaneous propagation is determined in real time during experimental recording for use in each study.
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2.3.4 Optical recording setup
The optical recording setup for the imaging data presented here has been described in a previous study (34). To summarize, to optically record from the VSFP-Butterfly 1.2 transgenic mice, a filter set was used to target mCitrine. The recording optics include the following filters and splitter: FF01-483/32-25 for mCitrine excitation (Semorck), FF01-
542/27 for mCitrine emission (Semorck), and 515LP as the beam splitter for mCitrine. A broad-spectrum LED light source (X-cite 120LED, Excelitas Technologies) was used during the experiment. For the calcium imaging experiments, the excitation filter was 488 nm, the emission filter was 520 nm, and the dichroic mirror had a separation wavelength of 516 nm (Semrock, USA). Optical images were acquired using a digital CMOS camera
(C11440, Hamamatsu Photonics) at a frame rate of 800 Hz (512 x 64 pixels, 4x4 binning).
The imaging data was analyzed with MATLAB and a signal process toolbox (MathWorks).
All the acquired image sequences were filtered using 4 × 4 spatial filters to eliminate electron noise from the camera and shot noise from the acquisition electronics. The fluorescent signals were presented as a percentage of fluorescent change, ΔF/F0, which was calculated as (F-F0)/F0, where F0 is the baseline fluorescence signal.
2.3.5 In vitro osmolarity to study the effect of cell distance on propagation speeds under 4-
AP conditions
To determine how extracellular space (osmolarity) affects the propagation speed and thus validating the role of the electrical field effect, we performed osmolarity experiments in vitro on longitudinal slices in 4-AP solution, as the propagation is usually very robust in that direction (12). The extracellular osmolarity was both increased and 44
decreased relative to the normal osmolarity condition. The control 4-AP solution was the same as described above. For low osmolarity experiment, 150 mL of deionized water and
15 µM of 4-AP were added into the control 4-AP solution, resulting in a 15% dilution and a 10% decrease in osmolarity. For high osmolarity experiment, 30 mM of D-Mannitol was added to the control 4-AP solution, causing an increase in osmolarity by 10%. Each osmolarity experiment (control, low, and high) started with the tissue being exposed to the control 4-AP solution for 30 minutes and field potential recorded from each trial. The high or low osmolarity solution was then introduced, and the field potential was recorded after
15 minutes of osmolarity change. The travelling speed of the spontaneous activity was measured by two recording glass micropipette electrodes (1.0 mm outer diameter and 0.5 mm inner diameter borosilicate glass filled with 150 mM NaCl solution) placed on the CA3 longitudinal hippocampal slices, and the speed was determined by the transit time between the electrode pair.
2.3.6 Extracellular electric field clamp
We have developed and tested a novel experimental system capable of clamping the extracellular electric field to zero locally, thereby preventing a neural signal from propagating by electric fields only. This device is based on the voltage clamp system commonly used for intracellular work but modified for extracellular fields. The circuit was validated and tested through computer modeling and benchtop testing under the aCSF solution (Fig. 2.3 and Fig. 2.4). The benchtop testing shows the field clamp system can cancel the measured voltage by applying appropriate current. A pair of extracellular recording electrodes were placed in the tissue to record the transverse electric field
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(direction parallel to the dendritic tree axis). Please see the supplemental document describing the derivation of the extracellular electric field clamp.
2.3.7 Isopotential experiment setup
Two recording electrodes (REC1 and REC2) were positioned along the cell layer of the hippocampal slice. An isopotential barrier/electrode was constructed from a single column of four 30 µm diameter tungsten electrodes that were positioned between the recording electrodes in the cell layer (Fig. 2.6A). This array of electrodes covered the soma and dendritic trees, which were then grounded in the bath.
2.3.8 Data and statistical analysis
Data collected from these studies were processed in MATLAB (MathWorks) for peak analysis and time-delay calculations (cross-correlation). During extracellular electric field clamp study, stimulus artifacts from the recording channels were removed by subtracting the feedback stimulation signal. A paired t-test statistical analysis was done under the two different conditions: propagation speed and amplitude. A statistical significance criterion of α = 0.05 was used for all tests. Results are shown as mean ± standard deviation of the mean.
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2.4 Results
2.4.1 4-AP-induced activity propagates along the longitudinal direction of the hippocampus
We studied the propagation of spontaneous epileptiform activity induced by 4-AP in rodent hippocampal slices in the longitudinal direction as the cells are tightly packed and arranged with soma and basal/apical dendrites parallel to adjacent cells (Fig. 2.1B,
2.1C). Spontaneous activity was observed in the presence of 4-AP, an epileptogenic compound that makes neurons hyper-excitable by blocking voltage-gated potassium channel (IA), as well as in a non-synaptic environment with low calcium aCSF (27, 90)
(Fig. 2.1D). To confirm that the activity observed was indeed propagating, direction and speed or the spontaneous waves were calculated. Propagation direction was determined from the sign of the time delay between recording electrodes. It was noted that activity propagated mostly from the temporal site to the septal site of the tissue (Fig. 2.1E, 125 of
135 events, 6 slices). Propagation speeds were estimated in the temporal and septal sides of the slice by measuring between REC1-REC2 (0.10 ± 0.04 m/sec) and REC2-REC3 (0.13
± 0.05 m/sec) respectively, with an overall mean speed of 0.12 ± 0.06 m/sec. There was no significant difference between the two speeds (Fig. 2.1F, 156 spikes, 6 slices) suggesting that the propagation speed is uniform. In addition, electrophysiology recording results were supported by optical recordings. Spontaneous activity images were captured in longitudinal hippocampal slices from transgenic mice that express the voltage sensitive fluorescent protein (VFSP-Butterfly 1.2) in the neuronal cytoplasm transgenic mice (113). These mice use calcium/calmodulin-dependent protein kinase II alpha (Camk2a) promoter to direct the
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expression of VSFP to pyramidal neurons by a Cre-mediated recombination system. The imaging field of view was on the hippocampal cell layer to capture the propagating wave while obtaining the largest region of observation (Fig. 2.1G). Fig. 2.1H shows sample image frames of the spontaneous epileptiform wave propagating through the hippocampus
(0.12 ± 0.01 m/sec, 60 events, 6 slices). Previous experiments and computer stimulation have suggested that events propagating at that speed do not require synaptic transmission
(12, 106).
2.4.2 Modifying the extracellular space changes propagation speed of 4-AP-induced activity in vitro
A previously published computational hippocampal network built purely with electric field coupling predicted that the speed of propagation should decrease with increasing distance between neurons (Fig 2.2A) (106). To test this prediction, we performed osmolarity experiments on longitudinal slices in 4-AP solution in vitro and found a similar relationship between the change in extracellular space volume and the resulting 4-AP-induced spike propagation speed. By decreasing the osmolarity of 4-AP aCSF (cell swelling and distance between cells decreases), the time delay between signals measured along the CA3 layer decreased from 10.12 ± 3.22 msec (n = 41 spike-pairs from
2 slices in normal osmolarity) to 4.53 ± 2.59 msec (p < 0.01, n = 73 spike-pairs from the same 2 slices in low osmolarity over 10 mins after dilution). With a measured distance between the two glass pipettes equal to 0.8 mm, a 125% increase in speed was obtained
(Fig. 2.2B). Conversely, by increasing the osmolarity of 4-AP aCSF (cell shrinkage and distance between cells increases), the time delay increased from 5.95 ±1.12 msec (n = 26
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spike-pair from 2 slices in normal osmolarity) to 9.76 ± 1.78ms (p < 0.01, n = 50 spike- pair from the same 2 slices in high osmolarity), corresponding to a 46.8% decrease in speed
(Fig. 2.2B). These results confirm the predictions of the model regarding the effect of cell- to-cell distance on the speed of propagation.
2.4.3 Canceling the endogenous electric field with an extracellular electric field clamp blocks propagation of epileptiform activity
We then hypothesized that a locally applied electrical field of equal amplitude and opposite polarity to that of an arriving wave should completely block the propagation of the wave. By clamping the extracellular field at zero, we determined whether endogenous electric fields are necessary for propagation of non-synaptic spontaneous activity. We, therefore, developed a technique to control the extracellular electric field with a clamping circuit capable of measuring the field of an arriving wave and applying current extracellularly to set it at zero (see Fig. 2.3, Fig. 2.4 for detailed methodology and validation of the clamping circuit). Extracellular electrodes were placed in the hippocampal longitudinal slice to record the transverse electric (direction parallel to the dendritic tree axis) (Fig. 2.5A). Spontaneous activity induced by 4-AP propagates through the cell layer as observed by the three recording electrodes (REC1 to REC3), traveling at a speed
~0.12±0.03 m/sec (Fig. 2.1D). Two extracellular stimulating electrodes were positioned outside the cell layer in the direction parallel to the longitudinal axis of the dendritic tree to generate the field. A pair of recording electrodes was positioned in the tissue to measure the electric field (REC2 and its reference electrode were used to measure the endogenous electric field for the clamp). A closed-loop feedback circuit was used to apply sufficient
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current to cancel the field in the tissue (see supplemental section for additional details).
With the clamp ON, spontaneous epileptiform waves appeared to stop propagating at REC2 as indicated by the lack of activity at distal electrodes REC2 and REC3 (located on the distal side of the clamp) (Fig. 2.5B). Spontaneous waves were still observed at the proximal electrode REC1 with the clamp is ON. Voltages were measured at all 3 recording sites before, during, and after the clamp was applied. Spontaneous activity reappeared and continued to propagate after the clamp was removed with no change in speed from before the clamp was applied. Normalized amplitude of the recorded voltages showed that during the application of the clamp, there was a significant decrease in amplitude in both REC2 and REC3 channels (Fig. 2.5C, n = 12 slices, t-test, p ≤ 0.01).
To further ensure that electric field coupling is a key mechanism in the propagation of spontaneous epileptiform activity, the electric field clamp was applied to the longitudinal hippocampal slice under non-synaptic conditions. Under low calcium (0.2 mM) aCSF, 4-
AP-induced epileptiform activity was observed to propagate in the longitudinal hippocampal slice from REC2 to REC3 (Fig. 2.5D). Since REC1 electrode was not affected by the electric field clamp, only two recording electrodes were used to test the field clamp under non-synaptic conditions. Again, voltages were recorded before, during, and after the extracellular electric field clamp was applied. With the clamp ON, activity was observed to be blocked (Fig. 2.5D). When the clamp was removed, activity reappeared and continued to propagate with no change in speed from before the clamp was applied. Analysis of amplitudes when the clamp was OFF or ON showed a significant decrease with the clamp on (n = 12 slices, t-test, p ≤ 0.01) (Fig. 2.5E). From these results, observing a block in
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propagation beyond REC2, supports the hypothesis that epileptiform activity is propagating in the hippocampus by electric field coupling alone.
Measurement of the speed of propagation in the proximal region with the clamp
ON from REC1 to REC2 shows a significant decrease from 0.09 ± 0.02 m/sec to 0.04 ±
0.01 m/sec (p <0.01) (Fig. 2.5F). It is not possible to measure the speed of propagation between REC2 and REC3 as the activity does not propagate between the two electrodes when the field clamp is ON. This result indicates that the applied field slows down the incoming wave as expected from the anti-field.
The derivation of the closed-loop control system of the electric field (see Fig. 2.3) indicates that changing the feedback gain should affect the amplitude of the suppression.
By increasing the feedback gain (5, 20, 50, 100 (µA/V), it was indeed observed that the amplitude of the propagating wave (REC2 and REC3) was significantly reduced in amplitude with a feedback gain of >20 µA/V (p < 0.01) (Fig. 2.5G). However, the amplitude recorded at the proximal electrode REC1 was not significantly affected suggesting that the clamping effect is local and did not affect the location of the source of the incoming wave.
2.4.4 Increasing the conductivity along the cell layer decreases the magnitude and propagation speed of epileptiform activity
Another way to cancel the electric fields generated by neural activity is to decrease the resistivity of the solution locally. We hypothesized that if the spontaneous activity is indeed propagating by electric fields, then increasing the conductivity within the tissue
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should significantly affect the amplitude of the electric field on the distal side. Two recording electrodes (REC1 and REC2) were positioned along the cell layer of the hippocampal slice. A high conductivity array was constructed from a single column of four
30 µm diameter tungsten electrodes positioned between the recording electrodes in the cell layer (Fig. 2.6A). This array of electrodes penetrated the soma and dendritic trees, which were then grounded in the bath. With the high conductivity region applied, the magnitude of propagating activity decreased at both recording sites (Fig. 2.6B). Propagation speed before the application of the high conductivity array was measured to be 0.16 ± 0.05 m/sec
(n=130 spikes, 4 slices), but significantly decreased to approximately 0.04 ± 0.01 m/sec
(Fig. 2.6C, p<0.01, n=100 spikes, 4 slices). Analysis of the amplitude showed a significant decrease in amplitude in both recording channels when the isopotential array was inserted
(Fig. 2.6D, p<0.05). With the high conductivity array inserted, amplitudes recorded by
REC1-2 decreased by 48% and 84% respectively. These results indicate that a high conductivity in the extracellular space did not block the propagation, but can affect both the propagation speed and the amplitude of the propagating event.
2.4.5 Applied electric fields can trigger self-propagating waves in the longitudinal hippocampal slice
The experiments reported above indicate that the wave is self-propagating whereby activated neurons generate and electrical field that activates neighboring cells. To test this hypothesis, we then applied electric stimulation to the tissue with current producing electric fields amplitude similar to amplitudes observed during spontaneous propagation. Under a lower concentration of 4-AP aCSF (50 µM), two recording electrodes were positioned in
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the cell layer of the slice (REC1 and REC2). A pair of stimulating electrodes spaced approximately 1 mm apart was positioned on the temporal side of the hippocampus slice in line with the soma and apical dendrites (Fig. 2.7A). An electric field pulse of 2-7 mV/mm (0.5-2mA stimulation, 100-200 µsec pulse width) was generated to initiate activity in the hippocampus (114) with a duration similar to the spontaneous events. Electric fields were measured at the stimulation site as well as in the tissue during stimulation. An example of a 5 mV/mm field pulse generating a propagating wave is shown in Fig. 2.7B.
We then measured the endogenous electric field during a wave propagating through the hippocampus. These values are within the same range to the endogenous field we measured as well as what has been reported in literature (103, 105, 114) It was observed that the field generated by initiated activity (5.13 ± 0.88 mV/mm) was not significantly different to
4-AP spontaneous activity (4.99 ± 1.14 mV/mm), which was observed after increasing the concentration of 4-AP (100 µM) concentration in the same slice (Fig. 2.7C, 60 spikes, 5 slices). These waves initiated by an electric field propagated from REC1 to REC2 with an average delay of 11 ± 3 msec (corresponding to a propagating speed of 0.09 ± 0.03 m/sec,
50 spikes, 4 slices). When compared to spontaneous 4-AP activity, the delay was not significantly different (Fig. 2.7D). Taken together, these results support the hypothesis that the 4-AP-induced waves are self-propagating by electric field coupling.
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2.5 Discussion
This study focuses on the characterization of a new mechanism of propagation of neural activity in the brain. The average propagating speed of epileptiform events observed in this study is about 0.1 m/sec, and the results of these experiments indicate that endogenous electric fields play an essential role in the propagation of events at that speed.
Although electric fields with low amplitudes (1 to 5mV/mm) are known to be able to modulate neural membrane potentials (115), they are not thought to be strong enough to activate neurons. In more excitable tissue such as in the presence of 4-AP, these electric fields should be able to not only modulate, but also excite neural propagation.
One prediction is that by modifying the extracellular space, we are changing the strength of the endogenous field capable mediating the speed of propagation.
Computational simulations predicted that changing distance between neurons connect by electric field coupling could modify the propagation speed (106). In this study, in vitro experiments confirmed this prediction, whereby 4-AP-induced epileptiform activity in hippocampal longitudinal slices travelled faster when extracellular osmolarity was lowered
(cells swelling), and vice versa (Fig. 2.2B). This also matches with the relationship between osmolarity and propagation speed in low Mg2+-induced seizure activity in hippocampal
CA1 region (116).
Another prediction is that a wave propagating by electric field coupling requires that an applied electric field in its path should affect the speed and amplitude of propagation. Canceling the extracellular electric field created by an incoming event should block propagation. This experiment requires a way to record the electrical field and control 54
it. To achieve this goal, we modified the concept of intracellular voltage clamp (117) to build an extracellular electrical field clamp. This novel concept was tested and validated by showing that an electrical field can be clamped to zero in a specific location (see Fig.
2.4 for validation). When applied to the propagating waves, the clamp completely blocked the transmission of the events by canceling the incoming field. Another possible mechanism for the effect is that the applied currents generated by the electric field clamp produce membrane hyperpolarization. However, based on the polarity of the applied current during the clamp, the source of the spike generation in the dendrites is depolarized not hyperpolarized.
Another method to decrease the effect of the electric field without affecting membrane polarization is to decrease the conductivity of the extracellular space. Results from experiments with a high conductivity array confirm the existence of an endogenous field as observed by a decrease in amplitude and propagation speed. The decrease of the amplitude and speed cannot be explained by damage to the tissue generated by the insertion of a high number of electrodes in the array since activity amplitude and speed returned to baseline levels following removal of the short-circuit electrode array. The fact that these experiments did not completely eliminate the propagation can be explained by the following two facts: 1) the spatial extent of the field is much larger than the electrode array and 2) the electrode array cannot generate a true short circuit between the neural sinks and sources in the tissue producing the electrical field since the interface between the metal and ionic solution is best modeled as a capacitor. Therefore, the net effect of the electrode array
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is to increase the bulk conductivity of the volume conductor thereby decreasing the amplitude of the fields.
A self-propagating wave was supported by the following experiment: stimulating temporal region of the intact hippocampus with known endogenous field strength (2-7 mV/mm) generated a self-propagating wave through the intact slice (Fig. 2.7). Applied stimulation could generate waves propagating at the same speed and amplitude as those propagating spontaneously thereby suggesting that the hippocampus cell network is capable of mediating self-propagating waves via small electric fields. This phenomenon was predicted by previous computer simulations (106) and validated experimentally in the present study.
The present study shows that the amplitudes of endogenous electric fields are high enough to generate spontaneous activity and further implies that 4-AP epileptiform can self-propagate by triggering new activity in the neighboring region through electric field coupling. Moreover, the present study shows that cancelling the fields generated by the epileptiform activity can prevent the propagation and thus we can infer that these fields are required to sustain the propagation. Therefore, the experimental results in this study support the notion that epileptiform activity can propagate through the electric field coupling alone. However, the interaction between soma and dendrites to generate electric fields or the intracellular response to these fields are still not clear. Previous computational modelling suggests that NMDA receptors are involved during this process (34).
A possible mechanism of propagation mediated by electric field coupling in the hippocampus is illustrated in Fig. 2.8A. In the presence of 4-AP, groups of neurons become
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more excitable and generate epileptiform activity (Fig. 2.8B). As the group of neurons depolarizes, a large sink is created in the dendrites by NMDA inward currents (24). The resulting extracellular field produces an outward current in the dendrites (source) in neighbor cells as well as a passive inward current (sink). This passive sink can be observed in the somatic region of the slice preceding the wave (Fig. 2.8C). The passive membrane depolarization then activates inward NMDA current activating those same cells. This process repeats itself, thereby generating a self-propagating wave. This source-sink relationship between soma and dendrites has been previously investigated by others (1, 39,
118–121), but will need to be validated experimentally in the future.
This study showed that the neural activity can propagate by a non-synaptic mechanism of electric field coupling based on several experimental results. This non- synaptic mechanism could explain how micro-seizures could possibly recruit neurons through large areas of the brain to generate larger seizures (122). In addition, this mechanism could explain the low success rate of multiple subpial transections, a therapy by which make several cuts in the cortex to isolate the epileptogenic zone (123). In principle, this treatment course prevents epileptic activity from spreading out. However, the outcome of this procedure is poor, and the long-term effects are still questionable. Only
33% of patients are seizure-free after receiving MST treatment in adults, and about 33-42% of patients are seizure free in children (124–126). The results of these studies could be explained by the electric field coupling phenomenon described above. It should also be noted that the non-synaptic coupling has been previously observed between hippocampal neurons but was attributed to gap junctions without clear evidence (127). Furthermore, we
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describe a novel technique (field clamp) for cancelling the endogenous electric field that could be used for treating non-synaptic epilepsy in humans.
In summary, this study is focused on the characterization of a new mechanism of propagation of neural activity in the brain. The results provide direct experimental evidence that 1) endogenous fields are more significant than previously thought, 2) electric field coupling can explain propagation in certain types of epileptiform activity in the brain, and
3) electric field coupling can explain the existence of self-propagating waves in the hippocampus.
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2.6 Figures
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Figure 2.1: Spontaneous epileptiform activity propagating in the longitudinal
hippocampal slice preparation
(A) Anatomical structure of rodent hippocampus. A single hippocampus is extracted and oriented for slicing along the longitudinal axis. Slices are cut at 400 µm thickness. Please refer to the previous publication for more details(12, 106). (B) Sample longitudinal hippocampal slice stained for cresyl violet blue that shows the pyramidal cell layers as dark blue lines CA3 cell layers observed along with positioning of recording electrodes. (C)
Insert: confocal imaging showing overall architecture of the longitudinal slice. Dark blue stain is the somatic layer while green stain are the dendritic branches. (D) 4-AP initiated spontaneous activity from CA3 cell layer. REC1 (black) leads REC2 (red), which leads
REC3 (green) in the direction of propagation. (E) Analysis of propagation direction. Each box represents the number of events. The size of the arrow indicates how many events propagate with respect to direction (T to S, or S to T). 125 out of 135 events propagate from temporal to septal (blue arrow) region of the hippocampus (n = 6 slices). (F) Analysis of propagation speed shows that there is no significant difference between REC1-REC2
(0.10 ± 0.04 m/sec) and REC2-REC3 (0.13 ± 0.05 m/sec) (80 spikes, 4 slices). (G) Setup for optical imaging region of interested using VSFP-Butterfly 1.2 transgenic mice. (H) An example of a 4-AP-induced wave from voltage imagining showing that a spike propagated from the temporal site to septal site in the hippocampus.
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Figure 2.2: Modifying extracellular space changes 4-AP propagation speed
(A) Effect of distance between cells on the speed of propagation in silico. Using 퐝퐜−퐜=3μm as control group, propagation speed increased when 퐝퐜−퐜 decreased, and decreased when
퐝퐜−퐜 increased. Modeled by Chen Qiu (106) (B) Effect of osmolarity on speed of propagation in vitro. Compared to activity in normal osmolarity of the 4-AP solution, propagation speed increases at low osmolarity (cell swelling and decreased cell-to-cell distance) and decreased at high osmolarity (cell shrinking and increased cell-to-cell distance).
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Figure 2.3: Derivation of extracellular electric field clamp circuit
(A) Voltage measured between the soma and apical dendrites (VA) is measured by amplifier G, and its amplitude is compared to a known value of the differential amplifier
(zero in this case). The voltage difference is amplified, converted in a current and applied as a feedback current (IA) that is generated by a V/I stimulus isolator. (B) Derivation of the feedback electric field clamp equation indicating how that the external electric field goes to zero with large feedback gain.
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Figure 2.4: Benchtop testing of extracellular electric field clamp
(A) Experimental setup of electric field clamp in an aCSF bath. Tungsten stimulating electrodes and glass recording microelectrode were placed in the tank. A 2 Hz sinusoidal wave was inserted in the bath. REC1 was used to measure voltage near stimulating electrodes. Voltage difference between REC2 and the reference was measured by the amplifier and used for feedback stimulation. (B) Waveforms without feedback are in phase as expected throughout the tank. (C) With feedback stimulation, REC1 amplitude decreases by 90% due to feedback stimulation while REC2 amplitude is zero indicating that the electric field has been canceled at the feedback stimulation site.
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Figure 2.5: Extracellular electric field clamp in vitro
(A) Diagram of the extracellular electric field clamp set-up. This circuit forces the extracellular electric field within the cell layer to be set equal to near zero depending on the gain of the feedback loop. Neural activity propagates from REC1 to REC3. REC2 signal is used as the feedback signal for stimulation. (B) 4-AP-induced spontaneous activity propagating from REC1 to REC3. With the electric field clamp turned ON the amplitudes of the spikes in REC2 and REC3 decreased. (C) Normalized amplitude of voltages recorded at each recording site with and without electric field clamp ON. A significant decrease in amplitude observed in both REC2 and REC3 (** p ≤ 0.01). (D) Extracellular
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electric field clamp in the presence of a pre-synaptic blocker (low calcium aCSF). Since there was no effect on REC1 with the clamp ON, only REC2 and REC3 electrode were measured for this set of experiments. 4-AP/low calcium-induced spontaneous epileptiform activity propagating from REC2 to REC3. With electric field clamp turned ON, the amplitudes of the spikes decreased in REC2 and REC3. (E) Normalized amplitude of voltages recorded at each recording site with and without electric field clamp ON. A significant decrease in amplitude observed in both REC2 and REC3 (** p ≤ 0.01). (F) 4-
AP initiated propagation speed decreases during stimulation (p < 0.01). (G) Effect of varying the feedback gain of electric field clamp on spontaneous activity. Normalized amplitude of propagating signal during stimulation with variable feedback. REC1 is not significantly affected by the changing feedback while REC2 and REC3 see a significant reduction in amplitude after 20 µA/V (p<0.01).
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Figure 2.6: High conductance arrays decrease speed of propagation
(A) Schematic of the experimental setup: an array of tungsten microelectrodes is placed within the tissue to create an equipotential line at zero volts in a direction parallel to the axis of the dendritic tree. (B) Example recording with array inserted (green arrow) and then removed after some time (red arrow). A decrease in amplitude is observed during isopotential application. (C) The average speed of activity decreased significantly when array applied (** p ≤ 0.01). (D) Measured a significant decrease in amplitude when the array is applied (REC1: 48% decrease, REC2: 84% decrease).
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Figure 2.7: Applying an electric field of similar endogenous amplitude induces a
propagating neural wave
(A) Schematic of the experimental setup: Electric field generated on the temporal side of the tissue with two stimulating electrodes placed 1mm apart. (B) Stimulation with an electric field set at 5mV/mm induces a propagating wave observed going from REC1 to
REC2. (C) Measured endogenous electric fields generated by a stimulating field is not significantly difference when compared to electric fields from 4-AP-induced activity. (D)
Analysis of the wave propagating shows no significant difference in delay (conduction velocity) between REC1 and REC2 under both spontaneous activity and initiated activity.
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Figure 2.8: Electric field coupling mechanism
(A) A group of pyramidal cells (1st group of cells in red) become excitable and depolarize in the dendritic tree (NMDA dependent), creating a current sink in the dendrites. An electric field is generated between the soma and the dendrites in the extracellular space (green dipole). This electric field passively depolarizes the neighboring neurons (cells in blue) as indicated by the blue dipole, and the cycle repeats. (B) Sample extracellular recording of spontaneous epileptiform activity in the longitudinal hippocampal slice. (C) 4-AP wave characteristic in the soma region. The passive sink (blue arrow) proceeding the active spike depolarization (green arrow) can be observed.
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Chapter 3: Epileptiform waves propagate through a physical cut solely by self-
sustaining electric fields
Parts modified with permission from Experimental Neurology, 2019, Vol. 317, July 2019, pp. 119-128; Copyright© Elsevier Publishing Self-propagating, non-synaptic epileptiform activity recruits neurons by endogenous electric fields Rajat S. Shivacharan*, Chia-Chu Chiang*, Mingming Zhang, Luis E. Gonzalez- Reyes and Dominique M. Durand
Note: Parts of this chapter will be submitted for publication as: Rajat S. Shivacharan, Chia-Chu Chiang, Xile Wei, Muthumeenakshi Subramanian, Nicholas H. Couturier, Dominique M. Durand. Spontaneous seizures can propagate by electric field coupling in vitro and in vivo *These authors contributed equally
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3.1 Abstract
Several experimental results have shown that epileptiform activity in rodent hippocampi propagates at a speed of ~0.1 m/s. 4-AP-induced waves propagate independently of synaptic transmission and gap junctions at a speed outside the range of ionic diffusion and axonal conduction known values. Recent studies suggest that weak endogenous electric fields can activate neurons, thereby generating a self-propagating wave that can propagate through cut or damaged tissue. Using both in vitro and in vivo electrophysiology, we tested the hypothesis that neural recruitment during seizures can take place purely by ephaptic coupling. The results show seizure-like activity self-generate and recruits neighboring neurons to create a self-propagating wave through a transection/cut in the hippocampus. This self-generating seizure like activity could propagate through the cut at a speed of ~0.11 m/sec which was not significantly different with or without a cut. We further show that these endogenous fields are self-sustaining through a cut with no significant difference in the field amplitude proximal to the cut, within the cut, or distal to the cut. These results suggest that electric field coupling is a sufficient mechanism to drive epileptiform activity and could explain the low success rate of surgical transections in epilepsy patients.
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3.2 Introduction
Epilepsy is one of the most common neurological disorders with an incidence and prevalence of about 0.05% and 1%, respectively (128). Mesial temporal lobe epilepsy
(MTLE) is most common cause of intractable focal epilepsy and the most frequent indication for epilepsy surgery (129). The hippocampus is a common focus of temporal lobe epilepsy (TLE) and is also involved in memory consolidation (31, 130). Temporal lobectomy is the current gold standard for the treatment of intractable TLE (131). However, even though the current gold standard treatment of refractory TLE is temporal lobectomy, the potential memory deficits caused by resections cannot benefit all candidate patients, especially patients with good memory scores and non-lesional hippocampi (132–134).
The hippocampus contains two types of orthogonal circuits: the transverse lamellae that are made of the trisynaptic pathway and the longitudinal pathway that runs along the longitudinal axis (temporal to septal pole) of the hippocampus (Fig. 3.1A) (41). The transverse lamellae are organized in parallel loops that originate and end in the entorhinal cortex and are important for memory processing (46, 47). The longitudinal pathway has been found to be important for synchronization or seizures (54). Furthermore, it has been shown that generalized cortical seizures arise from propagation of epileptiform activity along the longitudinal pathway(25, 57). Therefore, as an alternative to surgical resections, multiple transections are made to isolate the epileptogenic zone (59, 124–126, 135). In principle, this treatment course prevents epileptic activity from spreading out. However, the outcome of single or multiple transections is poor in some cases with epileptogenic zone often expanding beyond transection area, and the long-term effects are still
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questionable (59, 124–126). Only 33% of patients are seizure-free after receiving multiple subpial transection treatment in adults, and about 33-42% of patients are seizure free in children (124–126).
In the hippocampus, epileptiform activity has been observed traveling in both the transverse and longitudinal temporal-septal axis in both in vitro models and human patients
(12, 42, 110). Although synaptic transmission is required for seizure recruitment over long distances, several studies have shown that seizures can remain with impaired synaptic transmission (64, 90, 136). Such non-synaptic mechanisms include gap junctions between neurons (136), ion gradients and diffusion (35, 90, 92, 137, 138), astrocyte signaling (139–
141), and ephaptic (or electric field) coupling (12, 26, 34, 106, 142). Studies from our laboratory have shown that both epileptiform and slow wave sleep activity can travel non- synaptically at an approximate speed of 0.1 m/sec in the hippocampus by a mechanism consistent with ephaptic, or electric field coupling (26, 28, 106, 142).
It has been shown experimentally that weak electric fields can modulate neuronal firing in the cortex (97, 115). Furthermore, electric field have been suggested as a mechanism involved in modulating neural activity in several regions of the nervous system
(105, 143, 144). Several studies suggest that weak electric field can modulate neural activity in cortical and hippocampal networks (101, 102, 145). In hippocampal slices, electric field can affect the excitability of pyramidal cells and the synchronization of the hippocampal network (102, 145–147). In the cortex, weak electric fields have been shown to modulate slow rhythmic activity (101). Recent studies carried out in our laboratory have shown that electric field coupling is involved in self-propagating, non-synaptic
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epileptiform waves travelling at a specific speed of 0.1 m/sec in the hippocampus (142) and can mimic the progression of human seizures (34).
However, it is not known if electric field coupling is involved in the propagation of non-synaptic seizure-like activity. The purpose of this study is to provide computational and acute in vitro/in vivo experimental evidence suggesting that electric field coupling alone is capable of mediating non-synaptic seizure like activity within the hippocampus.
This study also aims to investigate the role of electric field coupling in the poor success rate of surgical transections for the treatment of epilepsy.
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3.3 Materials and Methods
3.3.1 Acute in vivo transection and recording experimental design
Acute in vivo experiments were conducted in male and female Sprague-Dawley rats
(150-350g) with the guidelines reviewed and approved by IACUC at Case Western
Reserve University. The rats were anesthetized by delivering 2-3% isoflurane in a carbogen gas mixture (95% O2, 5% CO2) and mounted on a stereotaxic frame (Kopf Instruments).
Four recording electrodes (E363/2, Plastics One Inc) were implanted in the CA3 regions along the longitudinal direction (temporal to septal pole) of the hippocampus (Fig. 1A).
The position of these electrodes, which were based on coordinates acquired via a rat brain atlas (Paxions, 2007), are REC1 (bregma -4.6 mm, lateral 5.1 mm, depth 7.0 mm), REC2
(bregma -5.3 mm, lateral 5.4 mm, depth 4.6 mm), REC3 (bregma -2.5 mm, lateral 2.0 mm, depth 3.0 mm), and REC4 (bregma -2.0 mm, lateral 2.0 mm, depth 3.4 mm). REC1 and
REC2 electrodes were placed on the temporal sites, and the other two electrodes, REC3 and REC4, were placed on the septal sites of the hippocampus.
The seizure focus was created by injecting the above-mentioned 30 mM 4-AP aCSF cocktail containing 30 mM 4-AP, 1.2 mM CaCl2, and 0.6 mM MgSO4. in the temporal pole
(bregma -4.1 mm, lateral 4.6 mm, depth 8.0 mm) with a bolus injection of 0.5 µL every 20 minutes until continuous seizures (status epilepticus) were observed (Fig. 1B). After recording seizures for 30 minutes to establish a baseline, a stereotactic knife (M120
Retractable Wire Knife, Kopf Instruments) was inserted and used to make a complete cut of the hippocampus at the level 4.0 mm posterior to Bregma and the depth of 2.0-4.5 mm below the skull (Fig. 1C). The knife severed the hippocampus unilaterally in the transverse
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direction which was about 45 degrees to the sagittal plane. The position of transections was in the middle of the four recording electrodes (between REC2 and REC3), and therefore two electrodes can be used to monitor the propagation of seizures both in the temporal and septal regions (Fig. 1D). The seizures started to propagate through the transection within
30 minutes based on preliminary results. Therefore, a 2-hour post-transections period of the recording was performed to capture epileptiform/seizure activity propagating along the four recording electrodes. All neural signals were acquired continuously and at a sampling frequency of 20 kHz (PowerLab, AD Instruments), amplified 1000 times (Model 1700, A-
M systems), and band pass filtered (0.1 Hz – 9 kHz). Histology was performed post experiment to confirm electrode placement and weather a complete cut was made.
Pre-processing of the acquired data was performed using digital filters, Butterworth band pass filter of 1-100 Hz and a Notch filter to remove the 60 Hz. Each individual spike from all four electrodes was isolated on the processing platform, MATLAB (Mathworks) to extract parameters such as the peak-to-peak amplitude and the temporal location of the spikes. The speed of propagation was calculated by determining the delay between the spikes and dividing by the distance between recording electrodes. Two methods were employed in this delay calculation, comparison of the spikes using cross correlation and phase difference(18).
3.3.2 Longitudinal hippocampal slice preparation
Experimental protocols were reviewed and approved by the Institutional Animal
Care and Use Committee (IACUC) at Case Western Reserve University. CD1 mice from
Charles River or VSFP-Butterfly 1.2 transgenic mice (for imaging) from The Jackson 75
Laboratory of either sex aged P10-P20 were anesthetized using isoflurane, and upon decapitation, the brain was place in ice cold (3-4 °C) carbogen mixture (95% O2, 5% CO2) sucrose enriched artificial cerebral spinal fluid (aCSF) solution consisting of the following
(in mM): 124 NaCl, 3.75 KCl, 1.25 KH2PO4, 2 MgSO4, 26 NaHCO3, 10 D-Glucose, and 2
CaCl2. Longitudinal hippocampal slices were prepared as described from earlier studies carried out in our laboratory (26, 34, 106, 142). In short, the brain was then sectioned by removing the cerebellum and separating the two hemispheres along the midline. From each hemisphere, the hippocampus was extracted from the temporal lobe of the brain. The hippocampus was sliced via a vibratome (VT1000S, Leica Microsystems) in an oxygenated sucrose aCSF bath containing (in mM): 220 Sucrose, 2.95 KCl, 1.3 NaH2PO4, 2 MgSO4,
26 NaHCO3, 10 D-Glucose, and 2 CaCl2 at a thickness of 400µm and then transferred to a recovery chamber containing oxygenated aCSF. Slices were incubated for at least one-hour at room temperature (25 °C) prior to recording.
3.3.3 Electrophysiology recording setup in vitro
An interface perfusion slice chamber (BSC-ZT, Harvard Apparatus) that keeps the tissue viable with temperature control and oxygenation was used to conduct the in vitro extracellular and electric field recordings in this study. The longitudinal slice was transferred from the recovery chamber to the interface chamber that was oxygenated (95%
O2, 5% CO2) and had temperature controlled (32-34 °C) normal aCSF solution perfusing over the tissue slice. Glass recording electrodes were pulled to a resistance of 5 MΩ made from fire-polished borosilicate glass micropipettes (0.5 mm inner diameter, 1.0 mm outer diameter) filled with 150 mM NaCl solution. An Ag/AgCl wire connected the filled glass
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recording electrode to an HS-2A head stage with a gain on one (Molecular Devices). The reference electrode for the recording electrodes was placed parallel to the tissue slice in the aCSF solution environment. All signals were amplified using an Axoclamp-2A microelectrode amplifier (Axon Instruments), and low-pass filtered (5 kHz) with additional amplification (FLA-01, Cygnus Technology). The signals were then digitized at 40 kHz by a recording data acquisition unite (PowerLab, AD instruments), and stored in a computer for post-processing analysis using MATLAB (Mathworks).
3.3.3.1 Local field potential, electric field amplitude, and speed measurement in vitro:
To calculate the local extracellular field potentials, recording electrodes were positioned along the cell layer. To measure the endogenous extracellular electric fields in the cut, pairs of recording electrodes were positioned (one in the soma, and the other in the apical dendrite) in and surrounding the cut (proximal and distal to the cut) (Fig. XXB).
Electric fields were calculated by taking the difference between VDendrite and VSoma and dividing the difference by the distance between the recording electrodes. Propagation speeds were calculated by dividing the delay (calculated with cross-correlation) by the distance between recording electrodes.
3.3.4 Optical recording setup and image processing
The optical recording setup for the imaging data presented here has been described in a previous study (34). To summarize, to optically record from the VSFP Butterfly 1.2 transgenic mice, a filter set was used to target mCitrine. The recording optics include the following filters and splitter: FF01-483/32-25 for mCitrine excitation (Semrock), FF01-
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542/27 for mCitrine emission (Semrock), and 515LP as the beam splitter for mCitrine. A broad-spectrum LED light source (X-cite 120LED, Excelitas Technologies) was used during the experiment. Optical images were acquired using a digital CMOS camera
(C11440, Hamamtsu Photonics) at a frame rate of 800 Hz (512 x 64 pixels, 4 x 4 binning).
The imaging data were analyzed with MATLAB and signal process toolbox (MathWorks).
All the acquired image sequences were filtered using a 4 x 4 spatial filters to eliminate electron noise from the camera and shot noise from the acquisition electronics. The fluorescent signals were presented as a percentage of fluorescent change ΔF/F0 which was calculated as (F-F0)/F0, where F0 is baseline fluorescence signal.
3.3.5 Statistical analysis
Statistical analysis was performed by using Student’s t-test to compare propagation speeds and delay intervals only in two different conditions. For in vivo recordings, the speed data was not distributed normally, hence a non-parametric test for related samples,
Wilcoxon Signed Ranks Test was performed. Amplitudes across all four channels in vivo were normalized to the average amplitude of REC1 in each animal, and then averaged between all animals (4 rats), with a Student’s t-test to compare amplitudes in each recording electrode for before and after a cut was made. One-way ANOVA and post hoc Tukey’s
HSD test was used for comparison of electric field amplitudes. A statistical significance criterion of α = 0.05 was used for all tests. Results are shown as mean ± the standard deviation unless otherwise noted.
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3.4 Results
3.4.1 Seizure-like activity propagates through a physical hippocampal transection in vivo acutely
Spontaneous epileptiform activity was generated from a bolus injection of 4-AP cocktail in the temporal pole of the hippocampus (Fig. 3.1B). A total of four recording electrodes were used to map propagation across the entire hippocampus (Fig. 3.1A).
Activity appeared spontaneously and synchronized from the temporal pole, REC1, to the septal pole, REC4 (Fig. 3.2A). Once a transection/cut was made, propagate similar effect was observed across all four recording cites (Fig. 3.2B). Visually, it was difficult to observe a delay but using cross-correlation between REC1-REC2, REC2-REC3, REC3-REC4 a delay was observed between each recording electrode and then averaged for an overall delay for spikes analyzed before and after a cut was made (Fig. 3.2C). Before a cut was made, there was an overall average delay of 71.2 ± 10.1 msec (0.12 ± 0.04 m/sec, n = 400 spikes, 4 rats). After a cut was made between REC2-REC3, the overall average delay of
61.4 ± 8.1 msec (0.11 ± 0.05 m/sec, n = 400 spikes, 4 rats), was found to be not- significantly different (p > 0.1). Amplitudes of the synchronized seizure-like events in all four recording channels was recorded. It was found that there was no significant change in amplitude before and after a cut was made in REC1 and REC2 (p > 0.1) but a significant change in REC3 and REC4 (Fig. 3.22D, p < 0.1, n = 400 spikes, 4 rats). Following experimental recordings, all animals were perfused and a histology study was performed to confirm electrode placement and determine location/size of the transection (Fig. 3.2E).
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3.4.2 Spontaneous epileptiform activity propagates non-synaptically through a cut in vitro.
To test the hypothesis that 4-AP-induced epileptiform activity truly propagates non- synaptically in the hippocampus, a physical cut was made in vitro, severing all mechanisms that require physical neuron to neuron communication. Extracellular recording electrodes were placed in the septal and temporal regions to track the electrical activity (see Fig.
3.3A). 4-AP-induced waves were observed to propagate from REC1 to REC2 at a speed of approximately 0.1±0.01 m/sec (Fig. 3.3A, n=92 spikes, 6 slices). Once a baseline activity had been established, a cut was made across the entire hippocampal slice using a scalpel blade. To ensure that the cut was complete, the cut ends were separated and rejoined. It was found that separating the tissue greater than 400 µm resulted in activity still being initiated on one half of the slice with no activity observed on the other side of the cut (Fig. 3.3B, n= 60 spikes, 6 slices). Activity was recorded once the two sides were put back together and spontaneous activity was observed on the other side of the cut propagating in the same direction. The wave appears to propagate through the cut with a speed of 0.09±0.01 m/sec, similar to that observed without the cut (Fig. 3.3C, n=104 spikes, 6 slices). We then separated the tissue to test the robustness of the propagation by measuring activity as we increased distance between each half of the slice. Using a paired t-test, no significant difference in propagation speed was found before and after a cut has been made (Fig. 3.3D, p < 0.01). These results show that activity arriving at the proximal cut end can activate neurons on the distal end of the cut.
We then measured the electric field amplitudes capable of inducing a spontaneous propagating wave in the intact longitudinal hippocampal slice. Recording electrodes were
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positioned along the soma and apical dendrites, and extracellular voltages were measured
(Fig. 3.3E). Electric fields were calculated by taking the difference in voltages and dividing by distance. Endogenous electric field amplitudes were found to be in a range from 2-6 mV/mm (Fig. 3.3F) with a mean value 3.9±0.9 mV/mm (n=61 events, 5 slices).
3.4.3 Spatio-temporal dynamics of the epileptiform remain unchanged through a cut in the hippocampus in vitro
Using longitudinal hippocampal slices, we optically mapped 4-AP-induced epileptiform activity propagating through the slice (Fig. 3.4A). After a cut had been made with slices close together (≤ 400µm), we observed that epileptiform activy was indeed travelling through the cut from temporal site to septal site (Fig. 3.4B-G, n = 3 slices). We observed a strong membrane depolarization within the pyramidal cell layer and surrounding pyramidal dendrites. A comparision of the propagation delay between REC1 and REC2 in vitro (Fig. 3.4H) before and after a cut (≤400 µm gap) was made and showed no significant difference (Fig. 3.4I, p > 0.1, n = 90 spikes, 6 slices). Before a cut, the delay between REC1 and REC2 was 29.4 ± 2.7 msec (0.1 ± 0.01 m/sec). Following the cut, the delay between REC1 and REC2 was 29.4 ± 2.0 msec (0.09 ± 0.01 m/sec). These findings suggest that some epileptiform events are unaffected by a single transection and can self- propagate, non-synpatically, throughout the hippocampus.
3.4.4 Endogenous electric field can cross a cut and are self-sustaining activity in vitro
Endogenous electric fields from spontaneous epileptiform activity were measured crossing a cut in vitro (Fig. 3.5A). Electric fields were measured proximal to the cut, in the
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cut (gap ≤ 400 µm), and distal to the cut when epileptiform activity cross the cut. The endogenous extracellular electric field was calculated to be 5.6 ± 0.8 mV/mm (proximal to the cut), 4.8 ± 0.8 mV/mm (in the cut), and 5.3 ± 0.8 mV/mm (distal to the cut). These values were not significantly different from one another (Fig. 3.5B, p > 0.1, n = 60 spikes,
6 slices). Propagation speed of the local field potential (0.11 ± 0.01 m/sec) and the electric field (0.09 ±0.01 m/sec) were not significantly different (Fig. 3.5C, p > 0.1, n=30 spikes,
6 slices).
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3.5 Discussion
Although electric fields with low amplitudes (1 to 5 mV/mm) are known to be able to modulate membrane potentials (102, 115), they are believed to be too weak to activate neurons. We have shown previously that in more excitable tissues, such as in the presence of 4-AP or lowered extracellular Mg2+/Ca2+, these electric field can not only modulate but also excite neurons and generate a self-propagating wave (26, 142). In this study, we focus on the role of electric fields in the propagation and recruitment of the seizure like activity.
In particular, we tested the hypothesis that these fields can underlie self-sustained activity both in vitro and in vivo preparations.
In this study, we first investigated how seizure-like activity can expand beyond surgical transections in an acute in vivo model of mesial temporal lobe epilepsy. We first induced an epileptic focus in the temporal lobe of the hippocampus that generated spontaneous epileptiform waves that traveled across the entire hippocampus (along the temporal-septal axis). We then made a transection and observed that these seizure-like waves could travel through the cut (~400 µm gap) (Fig. 3.2). An analysis of the delay before and after the cut was done and showed no significant change, indicating that seizure induced spikes can recruit other neurons and travel at ~0.1 m/sec in the hippocampal network by a non-synaptic mechanism. It can be argued that seizures might go around the transection in large areas such as the cortex but that is not the case in the hippocampus since the delay of the seizure induced spikes along the longitudinal axis of the hippocampus was not significantly different with or without the cut.
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The results from these acute in vivo experiments suggest that the mechanism underlying this non-synaptic propagation through a gap in the tissue is similar to the previously reported electric field coupling since the observed propagation speed (~0.1 m/sec) matched recent in vitro results (26, 142). We studied this non-synaptic mechanism in vitro using novel optogenetic imaging and electrophysiology techniques (34, 113).
Using transgenic mice, with genetically encoded voltage indicators, we confirmed that these epileptiform waves do travel non-synaptically by crossing a complete cut in vitro
(Fig. 3.3 and Fig. 3.4). Furthermore, we observed that these waves produced self-sustained fields strong enough to excite neurons by observing endogenous field strengths in the cut, thereby recruiting neurons distal to the cut (Fig. 3.5). A comparison of the propagation speed before and after the cut showed no significant change suggesting that electric field coupling is necessary and sufficient to explain the wave propagation.
The effects of electric field coupling on neurons is highly dependent on the extracellular space (106). It has been reported that regulating the extracellular space can reduce epileptiform activity and seizures(106, 148, 149). Moreover, furosemide and bumetanide, two powerful diuretics that cause an increase in extracellular space, have been shown to block epileptiform activity in many animal epilepsy models and can even have antiepileptic effects on human subject (149–152). In our study, we modified the extracellular space in the hippocampus by making a physical cut, or transection.
Furthermore, we showed that spontaneous epileptiform activity could propagate at the same speed regardless if a cut was present or not present suggesting that only a fast propagating mechanism such as electric field is required.
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Assuming that the 4-AP-induced waves are self-propagating by electric field coupling, then they should be able to proceed through a complete cut of the tissue since that would show that 1) the wave generates an electric field capable of activating the cells on the other side of the cut and 2) the mechanism must be electric field coupling since other forms of propagation except for diffusion have been eliminated. Although diffusion can propagate through a cut, the speed of propagation through the cut is not compatible with this mechanism (92). The experiments reported above do show that propagation goes through a cut, strongly suggesting that the mechanism of propagation involves ephaptic or electrical field coupling. Furthermore, this endogenous field coupling mechanism makes strong predictions about the interaction between endogenous fields and neural tissue.
One prediction is that the amplitude of the electric fields involved in the propagation must fall within a range capable of modulating neural activity. It has been reported that extracellular electric fields can alter the activity of single neurons and/or network. Experiments have shown that uniform DC electric fields applied to neural tissue can modulate neural activity by hyperpolarizing or depolarizing cells (153, 154). Electric field coupling has also been shown to synchronize axons and allow for specific action potential timing (96, 103, 155). Endogenous electric fields are known to induce extracellular voltage changes of less than 0.5 mV and fields under 5 mV/mm (105). In the present study, we provide experimental evidence indicating that spontaneous epileptiform activity induced by 4-AP propagating in the hippocampus generate electric field amplitudes in the range of 2-6 mV/mm (Fig. 3.3F). These fields amplitudes are similar to those known to generate electrical field effect in the hippocampal slices, approximately 5 mV/mm (103,
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114), and in the cortex, approximately 4.5 mV/mm (101). The data presented in this study suggests that the amplitudes of the endogenous electric fields are sufficient to not only modulate neural activity in hippocampal neurons, but also to activate a wave through a small gap in the neural tissue.
These results taken together could explain how micro-seizures recruit neurons to generate larger cortical seizures (122). It is possible that a single micro-seizure can recruit neurons locally by electric field coupling but when synchronizing with other micro- seizures over long distances, both electric field coupling and synaptic transmission could be involved (54, 122, 156, 157). Additionally, as mentioned earlier, electric field coupling could explain why surgical transections are ineffective in isolating an epileptogenic zone
(123). We show that seizure like activity can propagate non-synaptically by electric field coupling and to block the synchronization of seizures across large tissue area, the strength of the field can be influence by the size of the transection. Our results show that to improve the success rate of surgical transection, cuts that create a gap greater than 400 µm is required or multiple transections are necessary (59, 135).
In summary, this study focused on the characterization of endogenous electric field coupling in the brain as a non-synaptic mechanism for neuronal communication. To our knowledge, we have presented clear evidence that seizure-like activity can cross a physical cut or transection in an acute in-vivo preparation and we show via in-vitro studies that these epileptiform waves can cross a cut solely by self-sustained endogenous electric fields.
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3.6 Figures
Figure 3.1: Acute in-vivo spontaneous epileptiform activity in the hippocampus
recording and transection/cut experimental design
(A) Anatomical structure of rodent hippocampus. Electrode placement along the longitudinal (temporal-septal) axis. Each recording electrode (REC1, REC2, REC3, REC4) were amplified and digitized. (B) Bolus injections 0.5 µL every 20 minutes of 30 mM 4-
AP aCSF cocktail were delivered via a microsyringe in the temporal pole proximal to
REC1. (C) Stereotaxic knife (M120 Retractable Wire Knife, Kopf Instruments) inserted
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in the middle of the hippocampus between REC2 and REC3. Once the cannula was lowered to the correct depth, the dial was turned clockwise to expose the microknife and once fully exposed, the cannula was pulled up. (D) Post-cut, once knife has been removed.
Hippocampus cut unilaterally between REC2 and REC3 in the transverse direction which was about 45 degrees to the sagittal plane. Please see Methods and Materials for exact coordinates of electrode, micro-syringe, and knife placement. Illustrations courtesy of
Tiffany Yang.
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Figure 3.2: Epileptiform activity propagates through a transection in-vivo acutely
(A) 4-AP-induced seizure-like activity propagates from REC1 (temporal pole) to REC4
(septal pole). Before cut insert: observe synchrony between REC1-REC2 and REC3-
REC4. (B) Seizure-like activity continues to propagate with a transection/cut between
REC2 and REC3. After cut insert: observe synchrony between REC1-REC2 and REC3-
REC4. Time delay between recording electrodes before and after the cut was mad was quantified with cross-correlation. (C) Analysis of overall average delay between the 4 recording electrodes show no significant difference before or after the cut was made (p >
0.1). (D) Analysis of the amplitude of seizure-like activity spikes before and after the cut
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shows no significant difference in amplitude in REC1 and REC2 (p > 0.1) and a significant difference in REC3 and REC4 (p < 0.1). (E) Histological slice post experiment shows a cut in transverse plane of the hippocampus with a gap no larger than 400 µm.
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Figure 3.3: Epileptiform activity propagates through a cut in-vitro
(A) Baseline recording of spontaneous activity propagating from REC1 to REC2. The average delay is 23.2 msec. (B) A physical cut is made across the entire slice using a scalpel and verified by separating the two halves to ensure that all connections have been severed.
The robustness of the cut was tested with one part of the slice pulled away until no synchronized activity was observed. This result indicates that activity is indeed propagating through the cut. (C) Tissue halves were then put back together, and activity was observed to be propagating from REC1 to REC2. The average delay is 29.4 msec. (D) Analysis of the average speed before and after cut shows no significant difference. (E) Schematic of the instrumental system used to measure the endogenous electric field. Two recording electrodes are positioned in line with the soma and apical dendrites, and the voltages are
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recorded. The voltage difference is divided by the distance between the electrodes to determine the electric field. (F) Histogram of the measured endogenous electric field from
4-AP-induced activity propagating in an intact longitudinal hippocampal slice (60 spikes,
4 slices).
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Figure 3.4: Spatio-temporal dynamics of 4-AP activity crossing a cut in-vitro
(A) Diagram of the optical imaging setup on a longitudinal hippocampal slice. Images were collected processed in the field of view focused on the cell layer. (B)-(G) Image frame capture of 4-AP-induced spontaneous activity propagating from the temporal pole to the septal pole with a cut in the middle. Epileptiform activity propagates through a physical cut with strongest membrane depolarization in the cell layer and the immediate surrounding dendrites. (H) Electrophysiology setup to measure propagation speed. Both optical imaging as well as extracellular recording electrodes (REC1 and REC2) were used to measure propagation speed. (I) Average delay of the epileptiform activity propagating through the longitudinal axis in-vitro. No significant difference in the delay.
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Figure 3.5: Electric field measurements of epileptiform activity crossing the cut in vitro
(A) Schematic for measuring and calculating electric fields from spontaneous epileptiform activity in-vitro. (B) No significant difference between the measured electric fields within the cut and proximal/distal to the cut. (C) Comparison of propagation speed between spontaneous activity (LFP) and the self-sustained electric field generated by the activity showed no significant difference.
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Chapter 4: Slow oscillation sleep waves can self-propagate non-synaptically by a
mechanism consistent with ephaptic coupling
Modified with permission from Journal of Physiology, 2019, Vol. 597, Issue 1 January 2019, pp. 249-269; Copyright© John Wiley and Sons Publishing Slow periodic activity in the longitudinal hippocampal slice can self-propagate non- synaptically by mechanism consistent with ephaptic coupling Chia-Chu Chiang*, Rajat S. Shivacharan*, Xile Wei*, Luis E. Gonzalez-Reyes and Dominique M. Durand *These authors contributed equally
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4.1 Abstract
Slow oscillations are a standard feature observed in the cortex and the hippocampus during slow wave sleep. Slow oscillations are characterized by low‐frequency periodic activity (<1 Hz) and are thought to be related to memory consolidation. These waves are assumed to be a reflection of the underlying neural activity, but it is not known if they can, by themselves, be self‐sustained and propagate. Previous studies have shown that slow periodic activity can be reproduced in the in vitro preparation to mimic in vivo slow oscillations. Slow periodic activity can propagate with speeds around 0.1 m/sec and be modulated by weak electric fields. In the present study, we show that slow periodic activity in the longitudinal hippocampal slice is a self‐regenerating wave which can propagate with and without chemical or electrical synaptic transmission at the same speeds. We also show that applying local extracellular electric fields can modulate or even block the propagation of this wave in both in silico and in vitro models. Our results support the notion that ephaptic coupling plays a significant role in the propagation of the slow hippocampal periodic activity. Moreover, these results indicate that a neural network can give rise to sustained self‐propagating waves by ephaptic coupling, suggesting a novel propagation mechanism for neural activity under normal physiological conditions.
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4.2 Introduction
Slow oscillations are traveling waves observed during slow wave sleep and characterized by a slow periodic activity less than 1 Hz (158). These slow oscillations are thought to be generated from network fluctuations between periods of intense synaptic activity (Up states) and almost complete silence (Down states) in the thalamocortical and cortical-hippocampal networks (159), and thought to be related to memory consolidation
(160). In addition to the cortex, slow oscillations have also been observed in the hippocampus (1, 39) possibly originating from the prefrontal region, spreading across the neocortex, and reaching into the hippocampus (1, 39, 158, 161). Therefore, slow oscillations are a general feature across cortical and hippocampal areas.
Slow oscillations have been observed to propagate with speeds around 0.1 m/sec throughout the cerebral cortex in vivo (162). This propagation speed is very similar to the speed of epileptiform activity induced by 4-aminopyridine (4-AP) in the hippocampus (also
~0.1 m/s) (12, 14, 34, 142). 4-AP-induced epileptiform activity has been shown to be self- propagating in the absence of synaptic transmission or gap junctions. The mechanism most consistent with the data is ephaptic coupling whereby a group of neurons generates an electric field capable of activating the neighbor neurons (12, 142).
It has been shown experimentally that weak electric fields, or ephaptic coupling, can entrain action potentials of neurons (97). Ephaptic coupling has been suggested as a mechanism involved in modulating neural activity from different regions of the nervous system (105, 143, 144) especially in the vertebrate retina (163) and in the olfactory circuit
(164). 97
Several studies also indicate that weak electric fields can influence the neural activity in the cortical and hippocampal network level (101, 102, 145). In hippocampal slices, weak electric fields can affect the excitability of pyramidal cells and the synchronization of the hippocampal network (102, 145). In the cortex, weak electric fields have also been shown to modulate slow periodic activity in the in vitro preparation (101).
Although endogenous electric fields are thought to be too weak to excite neurons, two recent studies suggest that weak electric fields are involved in the propagation of epileptiform activity at a specific speed of 0.1 m/sec (12, 106).
Slow periodic activity can be reproduced in the in vitro cortical slices to mimic in vivo slow oscillation by lowering interstitial ionic concentration (38, 165, 166) and can be modulated by weak electric fields (167). Therefore, ephaptic coupling could play a role in the propagation of this slow periodic activity. In this study, we test the hypotheses that the slow periodic activity in the hippocampus can propagate non-synaptically and ephaptic coupling is the most likely mechanism of propagation.
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4.3 Materials and Methods
4.3.1 Ethical approval
All experimental procedures performed in this study followed National Institute of
Health (NIH) animal use guidelines and were approved by the Institutional Animal Care and Use Committee (IACUC) at Case Western Reserve University (Approval protocol number: 2016-0044). Animals were housed in disposable cages in a 12-h light/12-h dark cycle and climate controlled room (22 oC) with free access to water and food. Mice were deeply anesthetized by isoflurane and then euthanized by decapitation.
4.3.2 Origin and source of the animals
CD-1 IGS mice (strain code: 022, Charles River) were used to perform the in vitro experiments of local field potential recording and calcium imaging. For the experiments of voltage imaging slow hippocampal periodic activity, VSFP-Butterfly 1.2 transgenic mice (B6.Cg-Igs7tm78.1(tetO-VSFPB1.2)Hze/J, The Jackson Laboratory, Stock number:
023528) were crossed with Camk2ka-Cre transgenic mice (B6.Cg-Tg(Camk2a-cre)T29-
1Stl/J, The Jackson Laboratory, Stock number: 005359) and Camk2a-tTA transgenic mice
(B6.Cg-Tg(Camk2a-tTA)1Mmay/DboJ, The Jackson Laboratory, Stock number: 007004).
Triple-transgenic mice were used for in vitro hippocampal slice studies were approximately
10-30 days old (P10-P30).
4.3.3 In vitro hippocampal slice preparation and recording
Mice of either sex were anesthetized by isoflurane and euthanized by decapitation.
The brain was removed rapidly from the skull and was put (0–5°C) in high-sucrose 99
artificial cerebrospinal fluid (S-aCSF) containing (in mM): sucrose, 220; KCl, 3.0;
NaH2PO4, 1.25; NaHCO3, 26; D-glucose, 10; MgSO4, 2; CaCl2, 2; and bubbled with a 95%
O2/5% CO2 gas mixture. The hippocampus was dissected from the brain, cut longitudinally in a thickness of 400 μm, and then incubated in a bubbled normal aCSF at room temperature containing (in mM): NaCl, 125, KCl, 3.75; KH2PO4, 1.25; D-glucose, 10, NaHCO3, 26;
MgSO4, 2; CaCl2, 2. After one-hour recovery, slices were transferred to the interface- recording chamber (Harvard Apparatus) or a bath-immersion recording chamber (Warner
Instruments) for the further experiments. The orientation of the hippocampal slice was traced from the time the hippocampus was dissected out of the brain. The cut was made from the side of the hippocampus (sagittal plane), and at least two cell layers either
CA1/CA3 or CA3/CA3 were observed in the slice (12). The slow hippocampal periodic activity was induced by immersing the slices in the half-Ca2+/half-Mg2+ aCSF at room temperature containing (in mM): NaCl, 125, KCl, 3.75; NaH2PO4, 1.25; D-glucose, 10,
NaHCO3, 26; MgSO4, 1; CaCl2, 1 (38). In some experiments, slices were immersed in half-
2+ 2+ Mg /low-Ca aCSF, containing (in mM): NaCl, 125, KCl, 3.75; NaH2PO4, 1.25; D- glucose, 10, NaHCO3, 26; MgSO4, 1; CaCl2, 0.2, to block synaptic transmission (12, 168).
In the interface-recording chamber, glass pipette recording electrodes were placed along the cell layer in the longitudinal hippocampal slice. The distance between electrodes was determined by a plastic grid mesh that had a fixed spacing of 0.4 mm, which was placed under the tissue slice. All signals were amplified using an Axoclamp-2A microelectrode amplifier (Axon Instruments), low-pass filtered (5 kHz field potentials) with additional amplification (FLA-01, Cygnus Technology), digitized at 40kHz sampling
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frequency by using a digitizer (PowerLab 8/35, ADInstrument), and stored in a computer for further analysis. In the bath-immersion recording chamber, one glass pipette recording electrode was used to record local field potential for comparison to optical signals. The signal was received on an amplifier (Axopatch 200B, Molecular Devices), with amplification at 100, digitized at 20kHz sampling frequency by using a digitizer (PowerLab
4/35, ADInstrument), and stored on a computer for analysis.
4.3.4 Optical recordings
The setup of the imaging experiments was described in a previous study (34).
Shortly, for the optical recording of VSFP-Butterfly 1.2, a filter set was prepared for the mCitrine. The recording optics included the following filters and splitter: FF01-483/32-25 for mCitrine excitation (Semorck), FF01-542/27 for mCitrine emission (Semorck), and
515LP as the beam splitter for mCitrine. A broad-spectrum LED light source (X-cite
120LED, Excelitas Technologies) was used during the experiment. For the calcium imaging experiments, the excitation filter was 488 nm, the emission filter was 520 nm, and the dichroic mirror had a separation wavelength of 516 nm (Semrock, USA). The images were acquired by using a digital CMOS camera (C11440, Hamamatsu Photonics) at a frame rate of 200 Hz (2048 x 512 pixels) for the experiments of calcium imaging and higher frame rate of 800 Hz (512 x 64 pixels, 4x4 binning) for the experiments of voltage imaging.
The imaging data were analyzed with MATLAB and signal process toolbox (MathWorks).
All the acquired image sequences were filtered using a 4 × 4 spatial filters to eliminate electron noise from the camera and shot noise from the acquisition electronics. The
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fluorescent signals were presented as a percentage of fluorescent change F/F0 which was calculated as (F-F0)/F0, where F0 is the baseline fluorescence signal.
4.3.5 Statistical analysis
Statistical analysis was done by using a t-test to compare the speeds and intervals only in two different conditions. One-way ANOVA and post-hoc Tukey HSD were used for comparisons of frequency and amplitude in the NMDA antagonist experiments. A statistical significance criterion of α=0.05 was used for all tests. Results are shown as mean
± the standard deviation of the mean unless otherwise noted.
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4.4 Results
4.4.1 Slow hippocampal periodic activity can propagate non-synaptically in the longitudinal hippocampal preparation
Although slow periodic activity was previously observed in the hippocampus, we first sought to generate slow periodic activity in an in vitro longitudinal hippocampal slice to provide a long propagation pathway. The hippocampus was dissected and cut longitudinally using a vibrating microtome, and then the slices were immersed in the half magnesium and half calcium aCSF (half-Mg2+/half-Ca2+ aCSF) known to induce recurrent slow periodic activity in the neocortex (38, 165). Recurrent spontaneous slow periodic activity was induced in this longitudinal hippocampal slice with a period of 3.5 ± 1.2 sec
(140 events in 7 slices from 5 mice, Fig. 4.1b), which was similar to that observed in the neocortex (period of 3.44 ± 1.76 sec (38)). Three electrodes were placed along the cell layer in the longitudinal hippocampal slice, and local field potentials were recorded to observe the propagating direction and speed of the activity (Fig. 4.1a). Analysis of the propagating waveforms reveals the waves could propagate along the septal–temporal axis of the hippocampus at speed between 0.03 and 0.25 m/sec with a mean value of
0.10 m/sec (140 events, Fig. 4.1c). Thus, the spontaneous slow hippocampal periodic activity propagates with speeds similar to other propagating waves shown to be non‐ synaptic (0.12 ± 0.03 m/sec) (12, 34).
The first step to study the propagation mechanism of the slow hippocampal periodic activity was to determine if the synaptic transmission was required to generate this travelling wave and sustain its propagation. To test the hypothesis that slow hippocampal
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periodic activity can propagate without chemical synaptic transmission, the hippocampal slices were initially immersed in the half‐Mg2+/half‐Ca2+ aCSF and then in the half‐
Mg2+/low‐Ca2+ aCSF. Orthodromic stimulation was applied to the Schaffer collateral fibers between the two cell layers of the longitudinal hippocampal slice. The evoked response was measured to assess whether the block of synaptic transmission was complete
(Fig. 4.2a). Perfusion of half‐Mg2+/low‐Ca2+ aCSF solution abolished the orthodromic evoked potential as the amplitude of the orthodromic evoked potential significantly dropped to 0.02 ± 0.03 mV, which was not significantly different from 0 in Fig.
4.2b (n = 30 events in 3 slices, t test, p < 0.01). However, the slow hippocampal periodic activity was not influenced by the low‐Ca2+ aCSF, and the temporal characteristics of slow hippocampal periodic activity are similar in both solutions (Fig 4.1b, 4.2c). Furthermore, the speed of the slow hippocampal periodic activity during the perfusion of the half‐
Mg2+/low‐Ca2+ aCSF was not significantly different from the speed obtained before synaptic block (Fig. 4.2d, n = 7 slices from 5 mice). This result shows that synaptic transmission is not involved in sustaining propagation of the slow hippocampal periodic activity.
4.4.2 Slow hippocampal periodic activity can activate neural tissue through a complete gap in the tissue
To confirm the absence of any role of synaptic transmission and to eliminate other forms of communication between neurons except for ephaptic coupling, we next examined the possibility that electric fields generated by pyramidal neurons could propagate through a cut in the tissue by activating other cells across a small gap of the tissue, thereby
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eliminating chemical, electrical synapses (gap junctions), or axonal transmission. Fig. 4.3a and 4.3b shows the propagation of the slow hippocampal periodic activity before and after the cut in the tissue. To ensure that the slice was completely cut, the two pieces of tissue were separated and then rejoined while a clear gap was observed under the surgical microscope. The slow hippocampal periodic activity could indeed generate an event on the other side of a complete cut through the whole slice (Fig. 4.3b). However, the slow hippocampal periodic activity failed to trigger the activity across the gap when the distance of the gap increased (Fig. 4.3c). The expanded window in Fig. 4.3d shows that the waveforms of the slow hippocampal periodic activity and the delay between two signals measured in recording electrodes 1 and 2 were similar. The speed of the slow hippocampal periodic activity across the tissue was not affected by the presence of the cut in Fig.
4.3e (t test, n = 36 events in 3 slices). Therefore, this experiment shows that slow hippocampal periodic activity can propagate along a cut tissue by activating cells on the other side without any chemical and electrical synaptic connections at a similar speed to those observed in the intact tissue.
4.4.3 Propagation of the slow hippocampal periodic activity requires dendritic activation
To develop an understanding of the processes involved in the propagation, we then mapped the spatio‐temporal dynamics of the slow periodic activity in the longitudinal hippocampal slices from transgenic mice that express the voltage‐sensitive fluorescent protein (VSFP Butterfly 1.2) in the neuronal cytoplasmic membrane (113). These transgenic mice use calcium/calmodulin‐dependent protein kinase II alpha (Camk2a) promoter to direct the expression of VSFP to pyramidal neurons by a Cre‐mediated
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recombination system. The imaging field of view was set on a single cell layer of the hippocampal slice ensuring that the longest possible region of observation was obtained.
Fig. 4.4a shows the relative size of the field of view within the whole hippocampal slice.
In addition to imaging the neural activity in the hippocampal slice from the VSFP detection, two electrodes were placed on both ends of the cell layer of the hippocampal slice for comparison. Fig. 4.4b shows the imaging data at different time frames, indicating that the slow periodic activity was initiated in the temporal area and propagated in two directions through the cell layer. The activity of slow hippocampal periodic activity was predominant in dendritic areas while the amplitude of activity in the somatic layer was relatively lower.
To further analyze the slow hippocampal periodic activity in the somatic and dendritic regions, optical signals from the two regions mentioned above were extracted individually, and the temporal patterns were reconstructed. Fig. 4.4c shows that slow hippocampal periodic activity generates higher fluorescence intensity change in the dendritic areas compared to the somatic regions. Since the decrease of fluorescence intensity was proportional to membrane depolarization (113), optical signals indicate greater depolarization in the dendrites than in the somata when the slow periodic activity passes through the region of interest in Fig. 4.4d (t test, P < 0.01, n = 42 events in 6 slices from 4 mice).
4.4.4 Dendritic NMDA spikes are involved in the generation of the slow hippocampal periodic activity
The maximum power of the fluorescence from slow periodic activity was shown to mostly originate in the dendritic areas (Fig. 4.4), and the NMDA receptor blocker ((2R)‐ 106
amino‐5‐phosphonovaleric acid; APV) was shown to abolish the slow cortical periodic activity in a previous study (38). We then tested the possibility that dendritic NMDA spikes were involved in the slow periodic activity using three previously used criteria (169). First, we tested the hypothesis that slow hippocampal periodic activity could be blocked by the
NMDA antagonist APV. Fig. 4.5a shows that slow hippocampal periodic activity was abolished when applying 50 μM APV, and the effect was reversed following washout of
APV. The frequency and amplitude of the slow hippocampal periodic activity decreased significantly following the application of APV and reached near zero values within 10 min in Fig. 4.5b (one‐way ANOVA and post hoc Tukey's HSD test, p < 0.01, n = 11 slices from 4 mice). Secondly, we tested the hypothesis that slow hippocampal periodic activity can exhibit an all‐or‐none property (169). If the slow hippocampal periodic activity has this all‐or‐none property, the probability distribution of the spike amplitudes will display two separate groups corresponding to when the slow periodic activity is detected or not detected. Therefore, the peak amplitudes of signals were normalized by average amplitude of events for each slice, scaled by the mean value of the amplitudes of total events, and pooled in a histogram when the slow hippocampal periodic activity was detected.
Similarly, the peak amplitudes of signals were also obtained every 3 sec to mimic the period of the slow hippocampal periodic activity and pooled when the slow hippocampal periodic activity was blocked by APV (Fig. 4.5c). The histogram of peak amplitudes shows two separate normal distributions with different mean values and standard deviation (F test of equality of variances, p < 0.05, n = 330 events in 11 slices). The bimodal distribution implies that the slow hippocampal periodic activity is dominated by two primary responses, spiking or not, indicating that the slow hippocampal periodic activity has an all‐or‐none 107
property. Finally, the third criterion is that NMDA spikes can induce a calcium transient in neurons (169), and therefore we tested the hypothesis that slow hippocampal periodic activity could also generate intracellular calcium transients. We carried out calcium imaging experiments with calcium dye (OGB‐1) to monitor if intracellular calcium concentration changed when the slow hippocampal periodic activity was induced by the half‐Mg2+/half‐Ca2+ aCSF (Fig. 4.5d). We found that the induced slow hippocampal periodic activity was accompanied by calcium concentration transients detected by the calcium dye with an amplitude of 0.15 ± 0.04% (n = 30 events in 3 slices from 3 mice, Fig.
4.5e). Taken together, these results support the notion that NMDA spikes are involved in the generation of slow periodic activity.
4.4.5 NMDA channels are involved in the propagation of the slow hippocampal periodic activity
Although NMDA is required for the generation of slow periodic activity, it may not be necessary for its propagation. It is also unclear what other channels are involved. First, we determined the sensitivity of propagation of the slow periodic activity to fast chemical
(AMPA and GABAa) and electrical (gap junction) neurotransmission. Second, we tested the sensitivity of the activity to NMDA blocker. Finally, we tested if NMDA itself can generate a propagating wave. To determine if AMPA, GABAa and gap junctions could affect the propagation, we first established slow periodic activity and then applied a solution of half‐Mg2+/half‐Ca2+ aCSF containing 10 μM CNQX (AMPA blocker), 100 μM picrotoxin (GABAa blocker) and 50 μM mefloquine (gap junction blocker). Two recording electrodes were placed to record activity (Fig. 4.6a). Based on experiments in three slices,
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the three blockers reduced the amplitude and the firing frequency of slow periodic activity
(Fig. 4.6c and 4.6d). However, the speed of the slow periodic activity did not change before and after the application of three different blockers (n = 45 events from 3 slices, Fig. 4.6b).
To determine the role of NMDA channels on the propagation of the activity, we used a microsyringe to apply 1 μL of 100 μM APV (NMDA antagonist) locally in the cell layer on the surface of the tissue between the two recording electrodes (REC1 and REC2).
Fig. 4.7a shows that the local application of APV briefly blocks propagation with activity returning shortly thereafter (n = 3 slices). We speculate that APV blocks propagation for a short period due to APV diffusing from the site of application. Following a bolus injection of APV, the slow periodic activity returns.
We also applied a drop of 20 µM NMDA to determine if a propagating wave could be generated bi-directionally. Local application of NMDA between the two recording electrodes (REC1 and REC2) induced NMDA oscillations (n = 3 slices). This experiment suggests that NMDA induced oscillations activity propagates in both directions (Fig. 4.7b and 4.7c).
4.4.6 Propagation of the slow hippocampal periodic activity can be influenced by increasing the extracellular space
Assuming that electric fields are involved in the propagation of slow periodic activity, the speed of the activity should be influenced by modulating the size of the extracellular space (12, 106). The diuretic furosemide has been shown to change the extracellular space and suppress epileptic activity (150). Therefore, we applied furosemide
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to the in vitro slice to determine the effect of extracellular space volume on speed of propagation. Two recording electrodes were placed in the hippocampal slice immersed in the half‐Mg2+/half‐Ca2+ aCSF to record the baseline propagation of the slow periodic activity (Fig. 4.8a). Following a baseline recording period, half‐Mg2+/half‐Ca2+ aCSF containing 2.5 mM furosemide was applied to increase the extracellular space. The results are shown in Fig. 4.8b and indicate that the amplitude of the slow periodic activity was reduced and the delay between two recording electrodes was increased. Statistical analysis shows that the speed of the slow periodic activity after application of furosemide was reduced by 30% in Fig. 4.8c (t test, p < 0.01, n = 60 events in 3 slices from 2 mice). The furosemide experiment supports the hypothesis that the extracellular space volume affects the speed of the slow periodic activity and that ephaptic coupling is involved in the propagation.
4.4.7 Slow hippocampal periodic activity can be simulated in silico by a hippocampal network model connected only with ephaptic coupling
The above in vitro experiments excluded possible mechanisms of propagation of the slow hippocampal periodic activity such as chemical synaptic transmission, electrical synapses (gap junctions) and axonal compound potentials, and suggested the electric fields are involved in the propagation. Therefore, we next tested whether ephaptic coupling could be directly responsible for the propagation of the slow hippocampal periodic activity
(please see Appendix A1 for complete model details). Based on our experimental results, we constructed a simplified neural network model with neurons capable of generating
NMDA spikes in the dendrites and coupled only by electric fields (see Fig. A1.1).
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Simulated extracellular recordings were obtained in the somatic layer by three virtual electrodes (1 mm spacing) located within the neural network model. The model was capable of reproducing the main features of the slow hippocampal periodic activity recorded in the longitudinal hippocampal slice (Fig. 4.9a). From the expended views of the simulated spikes in Fig. 4.9a, the delay times of three events of the simulated slow hippocampal periodic activity were about 21.7, 22.1 and 18.5 msec, respectively, corresponding to propagation speeds of 0.09, 0.09 and 0.11 m/sec, respectively. The simulated slow periodic activity matched the characteristics of the speed and the inter‐event interval after analyzing more simulated data. In vitro experimental data show that the slow periodic activity was characterized by a speed of 0.10 ± 0.03 m/sec and the inter‐spike interval of 3.50 ± 1.20 sec (140 events in 7 slices) while the simulated events propagated at a speed of 0.10 ± 0.02 m s−1 with a period of 3.40 ± 1.40 sec (57 simulated events) in
Fig. 4.9b and 4.9c. In the hippocampal network model, the slow hippocampal periodic activity self‐propagated and generated an electric field of ∼5 mV/mm, well within the range of observed endogenous electric fields (12, 101, 103, 106). We then analyzed the intracellular recordings in the simulated network (Fig. 4.9d and 4.9e). The transmembrane potentials of dendrites (Vmd) and soma (Vms) for three different cells (cell #50, 100 and 150 in the longitudinal direction) show NMDA action potentials (NMDA spike) are generated in the dendrites during the propagation of the event. In summary, these simulated intracellular recordings show that a wave of activity similar to slow periodic activity can self‐propagate in silico along the longitudinal hippocampal network solely by ephaptic coupling.
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4.4.8 Slow hippocampal periodic activity can be modulated by an applied electric field in the extracellular space in silico
The model shows that electric fields generated by neural activity can activate neighboring neurons and generate a self‐propagating wave. This is consistent with experiments reported above with a cut in the tissue. Moreover, many reports show that applied electric fields with amplitudes similar to endogenous fields can modulate neural activity (101, 102, 143, 145). Therefore, an applied anti‐field should be able to slow the wave or even block the propagation, leading to a testable prediction in the hippocampal network model. The electric field (E(t)) generated by an incoming wave was detected in the middle of the network (near cell 100), and a proportional current with opposite polarity was applied I(t) = K * E(t) on the nearby area with a variable negative gain (K). Without any applied field, the delay between two cell (cell #50 and 100) was 20.4 msec (K = 0, Fig.
4.10a). With anti‐field stimulation (K = −0.006), the delay increased to 38.4 msec. By varying the gain K to −0.012, the delay increased to 91 msec resulting in a decrease of the speed of 88% (Fig. 4.10b). Further increasing the strength of anti‐field stimulation
(K = −0.018, Fig. 4.10c), the event was blocked in the region where the anti‐field was applied. The membrane polarization of the cells near the site of the application of anti‐field
(cells 100–105 in Fig. 4.10d) was positive, indicating that the block is not generated by membrane hyperpolarization but by the cancellation of the incoming field. These simulation results show that endogenous electric fields can directly affect the network propagation speed and predict that a closed loop electric field clamping system should be able to block propagation of the slow hippocampal oscillation in the in vitro preparation.
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4.4.9 Propagation of the slow hippocampal periodic activity can be blocked by EEFC in vitro
An extracellular electric field clamp was implemented in an experiment to test the model's prediction that propagation of the slow hippocampal periodic activity can be influenced by extracellular electric fields. A closed‐loop system as shown in Fig. 4.11a was implemented whereby the electric field perpendicular to the direction of propagation generated by an incoming event of the slow hippocampal oscillation was recorded and clamped to zero by applying a regulated current using a proportional controller (see
Chapter 1 for additional details on EEFC). The slow periodic activity events propagating through the cell layer from recording electrode 1 to recording electrode 3 were blocked when the extracellular electric field was clamped to zero around recording electrode 2 (Fig.
4.11b). Fig. 4.11c shows that the extracellular field clamp was able to significantly reduce the amplitude by over 95% (P < 0.01, n = 120 events in 6 slices). This result indicates that the slow hippocampal oscillation can be blocked by an anti‐electric field strongly supporting the hypothesis that these waves propagate by ephaptic coupling. In addition, electric field with amplitudes within the range of endogenous field values (<5 mV/mm) could trigger a propagating spike at a speed similar to slow periodic activity (Fig. 4.11d- e, n = 30 events from 2 slices).
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4.5 Discussion
Slow oscillations have been widely observed in the thalamocortical network and cortical–hippocampal network (39, 161, 162, 170) and are thought to be related to memory consolidation (39, 171). Most studies have focused on the generation of the slow oscillations or the interaction between the cortex and the hippocampus during the wave sleep. Some studies have shown that slow hippocampal oscillations were accompanied by slow cortical oscillation activity (1, 39) or that the spontaneous activity in the entorhinal cortex modulated the slow hippocampal oscillation activity (172). Furthermore, it was shown that the slow cortical oscillations could be maintained without any connection between the hippocampus and the cortex (38, 173). However, the dependence between the slow cortical and hippocampal oscillations is not known. In the present study, we show that the in vitro slow hippocampal oscillation can be self‐sustained and self‐propagating in isolated hippocampus without any connections from the cortex.
We also provide in vitro experimental evidence indicating that the slow hippocampal periodic activity consists of self‐propagating waves that use ephaptic coupling as a means of propagation and are similar to epileptiform activity induced by 4‐
AP (12, 34, 106, 142). Several theoretical models describing travelling waves in the brain have been proposed (7, 174, 175). One such model explains propagation by weakly coupled oscillators connected by synaptic transmission with a travelling speed dependent on the oscillation frequency. However, the speed of slow periodic activity in the present study is consistently about 0.1 m/sec, and the slow hippocampal periodic activity can propagate without synaptic transmission (Figs. 4.2 and 4.3). Therefore, the propagation of this slow
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periodic activity cannot be explained by a weakly coupled oscillator model. Another propagation model proposes that the travelling wave is generated by a single oscillator outside the hippocampal network but also relies on synaptic connections to produce a propagating wave (7, 175, 176). A third theoretical model of the travelling waves proposes that the wave propagates from activation of nearby neurons connected by short axons along the networks thereby increasing the time delay (7, 175). All of the models mentioned above requires synaptic transmission, and therefore these models are not consistent with the data presented in this study. Here we propose a new propagation model whereby a wave can propagate by endogenous electric fields, instead of synaptic transmission, by activating neighbor neurons through ephaptic coupling.
There are other possible mechanisms to explain neural propagation without synaptic transmission. One possible mechanism is gap junction connections since gap junction channels have been found in the hippocampus (85). Gap junctions could be involved in the generation of waves in the hippocampus since a block of gap junctions reduced the theta wave power (177). However, gap junctions are known to exist between
GABAergic interneurons but are rare between pyramidal cells (178, 179). Also, it is unlikely that propagation through gap junctions should be influenced by the extracellular voltage since gap junctions provide a direct connection between connected cells.
Furthermore, the gap junction model cannot explain why the slow periodic activity could trigger activation of tissue on the distal side of a cut (Fig. 4.3). Another possible mechanism to explain non‐synaptic propagation is ionic diffusion. Extracellular potassium has been observed to diffuse in the hippocampus and is correlated to some neural waves (180).
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However, literature reports that neural potassium waves propagate at very low speeds
(0.00018 and 0.00084 m/sec) (90, 91, 180, 181) and therefore they cannot explain the propagation of the slow periodic activity with speed three orders of magnitude higher
(0.1 m/sec).
Another feature of propagation mediated by ephaptic coupling could be the propagating direction. Based on the structure of the longitudinal hippocampal slice, ephaptic coupling‐mediated activity should be able to propagate in both directions when the activity initiates in the middle of the cell layer. This feature was observed in the present study (Fig. 4.4b, 4.7b, and 4.9d) and in a previous study (28). Observation of the bidirectional propagation is highly dependent on where the activity initiated. The bidirectional propagation was observed occasionally using the voltage imaging set‐up, as shown in Fig. 4.4b. Therefore, to further address the directionality question, we applied
NMDA locally to show that once the activity is forced to start in the middle of the slice, it will propagate bi-directionally as predicted by an ephaptic coupling mechanism (Fig.
4.7b).
The results in Fig. 4.4 indicate that slow periodic activity is a self‐propagating event and that the mechanism of propagation most consistent with the data is ephaptic coupling.
Therefore, slow periodic activity propagation could be explained by a number of neurons generating electric fields and associated currents during an event capable of activating the dendritic trees of neighboring neurons thereby generating a self‐propagating wave.
Other in vivo studies also show that the maximum power of the slow oscillation activity is located in apical dendrites (39, 182). Moreover, electrically triggered slow oscillations in
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the hippocampus start with a wide activation at stratum lacunosum moleculare (182, 183).
These studies support that the generation of the slow periodic activity is within the dendritic areas and our results further show that this activity can be regenerated in the dendritic areas by ephaptic coupling. The propagation of the slow periodic activity predominantly depends on dendritic activity and extra-synaptic NMDA receptors since the slow periodic activity propagation persisted when blocked pre-synaptically (low Ca2+ aCSF) but was blocked by an NMDA antagonist (Fig. 4.2 and 4.5). The NMDA receptor has been shown to produce regenerative long‐lasting action potentials (NMDA spikes) in dendrites of central nervous system neurons (71). NMDA receptors can generate spikes independently of sodium channel activation in the soma but depend on glutamate known to be present in the extracellular space of brain slices (184). Therefore, our results indicate that in vitro slow hippocampal oscillations could self‐generate and self‐propagate through the activation of the NMDA receptors.
A computer model was built on experimental observations and simplified assumptions to show that NMDA channels and ephaptic connections could reproduce the propagation of slow periodic activity by electric fields alone. The simulated slow hippocampal periodic activity from the model was characterized by periodicity and speeds similar to those observed in vitro (Fig. 4.10b). The simulated slow hippocampal periodic activity could propagate by generating a weak electric field with amplitude within the range of endogenous fields as indicated by previous in vitro studies (12, 101, 103, 106, 142).
Several studies have shown that a weak electric field can affect or modulate the neural activity (101, 102, 143, 145). Yet, weak electric fields are thought to be too small to
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produce excitation directly (97). In the present study, both experimental and modelling results show that the electric fields in the range of endogenous fields are sufficient to excite neural tissue and to sustain a propagating wave without synaptic transmission.
Furthermore, applying a weak anti‐field is sufficient to block the propagation of the slow hippocampal periodic activity (Fig. 4.10 and 4.11). The weak electric field generated by slow hippocampal periodic activity during the conditions that simulate slow wave sleep are similar in amplitude to those previously reported under epileptogenic conditions, and both are consistent with ephaptic coupling (12, 106, 142). Therefore, in addition to providing new insights on the mechanisms underlying the propagation of slow periodic activity during slow wave sleep, these results could be relevant to the understanding of the effect of low amplitude fields generated by transcranial direct current stimulation to improve memory or control seizure frequency (185, 186).
The slow periodic activity reported in the present study is limited to the longitudinal hippocampal slice preparation, and is similar but not identical to other propagating events in the cortex (38, 187). The longitudinal preparation of the hippocampus has a dense laminar organization while the organization of the cortex is more heterogeneous.
Therefore, the results reported here cannot be applied to the mechanisms of propagation of the cortical slow oscillations, which likely involve synaptic transmission particularly for long‐range propagation in different brain regions (188–190). The spontaneous activity in the present study is generated by simply changing the concentration of ions to simulate a sleep ionic environment in vitro (38, 165). Ephaptic coupling has been shown to play an important role in the propagation of pathological events induced by 4‐AP (12, 142) and the
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present results confirm that similar mechanism can play a role in normal physiological conditions since the induced slow periodic activity is considered to be a physiological activity (38, 165).
In summary, the present study shows that the in vitro slow periodic activity, mediated by the NMDA spikes, can propagate non‐synaptically by a mechanism consistent with ephaptic coupling. This study implies that ephaptic coupling could play an important role in the propagation of neural activity under normal physiological conditions as well as in pathological situations.
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4.6 Figures
a c
15
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requency F
0 0.04 0 0.05 0.1 0.15 0.2 0.25 b Speed (m/s) 0.040.02 REC1 0.020 -0.02 020 30 40 50 60 70Expanded window -0.02 20 30 40 50 60 70 0.04 REC2 10 ms 16 ms 0.02 0.040 -0.020.02 0 -0.040.04 20 30 40 50 60 70 -0.02 5 s -0.040.02 mV 0.5 20REC3 30 40 50 60 70 0
-0.02 20 30 40 50 60 70 Figure 4.1: Slow hippocampal periodic activity propagation in vitro
(a) Illustration of the experimental setup. (b) Local field potential recordings in the
longitudinal hippocampal slice show slow hippocampal periodic activity propagating
longitudinally. (c) A speed histogram of slow hippocampal periodic activity indicates that
the propagating speed is around 0.1 m/sec similar to 4-AP-induced interictal spikes.
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0.5
0
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-2 a 1574 1576 1578 1580 1582 1584 1586 b1588 Orthodromic evoked responses 2+ 2+ 2+ 2+ 0.02 half Mg /half Ca half Mg / Low Ca 0.5 ** 0.01 0.5 0 0 1.0
-0.010 V
m -0.5 0.8 -0.02 -0.510 15 20 25 10 ms30 35 40 45 50 55 60 -1 0.6 -1 600 0.05 Orthodramic evoked -1.5 mV 0.4 -1.5 response 0 -2 0.2 2874 2876 2878 2880 2882 2884 2886 NS Stimulation artifact 2424 2426 2428 2430 2432 2434 2436 2438 -0.05 0 10 15 20 25 30 35 40 45 50 55 60 half Mg2+/ half Mg2+/ 0.02 c 2+ 2+ 0.01 Low Ca 0.04 REC1 half Ca 0.020
-0.01 0 d -0.02 -0.0210 15 20 25 30 35 40 45 50 55 60 10 15 20 25 30 35 40 45 50 55 60 0.20
0.05 REC2 0.15 0 0.10 -0.05
10 15 20 25 30 35 40 45 50 55 60 0.05 Speed Speed (m/s) 0.02 REC3 5 s
0.04 0.5 mV 0.01 0 2+ 2+ 0.020 half Mg / half Mg / -0.010 half Ca2+ Low Ca2+ -0.02-0.02 10 15 20 25 30 35 40 45 50 55 60 10 15 20 25 30 35 40 45 50 55 60
0.05 Figure 4.2: Slow hippocampal periodic activity can propagate without synaptic
0
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10 15 20 25 30 35 40 transmission45 50 55 60
0.04
(a)0.02 The orthodromic evoked potential is abolished under the low calcium condition. (b)
0
-0.02 The10 amplitude15 20 of 25 the evoked30 35 potentials40 45 decreased50 55 to60 near zero values under the low- calcium condition. **: p<0.01. NS: Not significantly different from zero. (c) Local field potential recordings under the low calcium condition show that the slow hippocampal periodic activity does not change the temporal features. (d) The speed values of the slow hippocampal oscillation in the half-Mg2+/half-Ca2+ aCSF and half-Mg2+/low-Ca2+ aCSF were not significantly different.
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a
b
c
d e NS
Before Cut After Cut Before Cut After Cut
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Figure 4.3: Slow periodic activity propagation along the tissue with a complete cut in
vitro
(a) Slow hippocampal periodic activity propagated from recording electrode 1(REC1) to recording electrode 2 (REC2) at a speed of 0.10 ± 0.01 m/sec before the cut. (b) A complete cut in the hippocampal slice. Slow hippocampal periodic activity was observed to be propagating along the slice with a cut from REC1 to REC2 with speed similar to that recorded in an intact slice by activation of the neurons of the other side of the cut. (c) Slow hippocampal periodic activity stopped propagating when the gap was 400 µm. (d)
Expanded windows of the single event of the slow hippocampal periodic activity before and after the cut revealing similar delays between two recording electrodes. (e) Speeds of slow hippocampal periodic activity before and after the cut. There is no significant difference between the two speeds. NS.: non-significance.
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a c 0.5 mm Cell layer Apical dendrites Optical signal (Df/f) dendrite
1 s b 1% soma Basal dendrite 0.5 mm Cell layer Apical dendrite
60 0 ms Cell layer 40 Fluorescent change 20 0.2-2.4 % 50 100 15030 200 250 d 60 6 ms Initiation ** 40 25 150 0.15 20 125 20 50 100 150 200 250 60 100 14 ms 0.1-1.2 % 40 15 75 20 10 50
0.05 Normalized 50 100 150 200 250
60 amplitude (%) 22 ms 5 25 40 0 % 0 20 0 50 100 150 200 250 soma dendrite 50 100 150 200 250 Figure 4.4: Transmembrane voltage imaging and the spatial-temporal features of the
slow hippocampal periodic activity
(a) Experimental setup for imaging experiments. (b) Imaging data show that the slow hippocampal oscillation propagates through the longitudinal hippocampus and the maximum power of the slow periodic activity was in the dendritic area. (c) The optical signals extracted from the somatic area (blue dot) and the dendritic area (red dot) show the amplitudes are different between these two areas and (d) reach significance. **: p<0.01.
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0.1 0.1
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-0.5 -0.5 a 0 20 40 60 80 100 120 20 40 60 80 100 120 140 Baseline Wash out (half-Mg2+/half-Ca2+ ) half-Mg2+/half-Ca2+ + APV (half-Mg2+/half-Ca2+) 0.1 0.1 0.1 0.1 0.1
0 0 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.2 20 s -0.3 -0.3 -0.3 -0.3 -0.3 0.2 0.2 mV -0.4 -0.4 -0.4 -0.4 -0.4 -0.5
-0.5 -0.5 -0.5 -0.5 20 40 60 80 100 120 b0 20 40 60 80 100 120 0 2020 4040 6060 8080 100100 120120 140 20 40 60 80 100 120 0.6 Frequency Amplitude NS NS 0.5 0.8 0.1 0.1 0.4 0 0 0.6 NS NS
-0.1 0.3 -0.1 mV Spikes/sec 0.4 -0.2 0.2 ** -0.2 -0.3 -0.3 0.1 ** ** 0.2 -0.4 -0.4 ** ** 0 0 -0.5 -0.5 (min) -15 -10 -5 5 10 15 5 10 15 -15 -10 -5 5 10 5 (min) 0 20 40 60 80 100 120 20 40 60 80 100 120 15 10 15 Baseline APV Wash out Baseline APV Wash out c No firing Firing e Field potential 80 70 60 50 2 s 40 0.2 mV 30
Frequency Optical signals (Df/f) 20 10 0 -0.1 0 0.1 0.2 0.3 0.4 0.5 Event peak (mV) d Calcium imaging
0.1 0.1 % 2 s electrode
Figure 4.5: Slow periodic activity dependent on NMDA and intracellular calcium
(a) Local field potential recordings in three different conditions, baseline (half-Mg2+/half-
Ca2+ aCSF), half-Mg2+/half-Ca2+ aCSF + NMDA antagonist (APV), and wash out (half-
Mg2+/half-Ca2+ aCSF), respectively. (b) Frequency and amplitudes of slow hippocampal
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periodic activity in these three different conditions. **:p<0.01. NS.: Not significant. (c)
Amplitude histogram of the peak of the slow periodic activity under conditions of baseline and APV in (a). (d) Calcium imaging obtained during the propagation of slow periodic activity. The blue dot indicates the position of the electrode. The red and black dots indicate the areas selected area to extract optical signals. (e) Optical signals from calcium imaging show the intracellular calcium concentration transients observed when the slow periodic activity was detected by local field potential recordings.
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a c half Mg2+ / half Ca2+ e
REC1 Expanded window mV
100 ms 0.3 0.3
REC2 3 s 0.5 0.5 mV b
d CNQX+PTX+Mefloquine f
REC1 Expanded window Speed (m/s) Speed
0.2 0.2 mV 100 ms 2+ REC2 3 s half Mg / CNQX+PTX 0.5 mV half Ca2+ +Mefloquine
Figure 4.6: Effects of CNQX, PTX, and Mefloquine on slow periodic activity
(a) The experimental setup. (b) The speeds of the slow periodic activity before and after application of CNQX, PTX, and mefloquine. (c) The slow periodic activity induced in half
Mg2+ /half Ca2+ aCSF. (d) The slow periodic activity after application of CNQX, PTX, and mefloquine.
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a Effect on local APV application Noise induced by local application of APV
REC1 Slow periodic activity
Recovery of the slow 10 s periodic activity
REC2 0.2 mV Blockage of propagation
b Effect on local NMDA application c Local application of NMDA REC1 Slow periodic Expanded window activity NMDA induced oscillation NMDA induced oscillation
2 s 0.5 mV 0.5
REC2 1 s 0.5 mV 0.5
NMDA induced oscillation
Figure 4.7: Effect of local APV/NMDA application on slow periodic activity in vitro
(a) The activity propagates from REC1 to REC2, and the local application of APV blocks the propagation shortly. (b) The local application of NMDA can trigger activity propagating in the both direction. (c) The expanded window shows that NMDA induced a small oscillation activity in the both recordings.
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a c **
b (%) speed Normalized half Mg2+/ Furosemide Baseline activity half Ca2+ REC1
Expanded window mV
100 ms 0.3 0.3
REC2 2 s 0.5 0.5 mV
Furosemide (2.5 mM)
REC1 Expanded window mV
100 ms 0.2 0.2
REC2 2 s 0.5 0.5 mV
Figure 4.8: Effect of modifying extracellular space on slow periodic activity in vitro
(a) Experimental setup. (b) The slow hippocampal periodic activity in the baseline and after the application of 2.5 mM furosemide. (c) The speed of the slow hippocampal periodic activity decreased by 30 % after the furosemide was applied (t-test, p<0.01, n=60 event in
3 slices). **: p<0.01. 129
a
Modeling
Experimental
0.1mV 0.5s
b c
Exp Model Exp Model d e
21ms Vmd Cell 50 Cell 100 Cell 150 Vms Cell 50 Cell 100 10mV Cell 150
50ms
Figure 4.9: Slow periodic activity propagating by electric field coupling in silico
(a) Representative examples of slow hippocampal periodic activity generated from the model (blue, green, and red traces) and recorded from the hippocampal slice (black trace). 130
The expanded-window figures show three separate events of simulated slow hippocampal oscillation with speeds of 0.092 m/sec, 0.091 m/sec, and 0.108 m/sec respectively. (b-c)
Comparison of the intervals and speeds of the slow hippocampal periodic activity obtained from a computational model and experimental data shows no significant difference between model and experiments. (d) Simulated intracellular membrane potentials on the dendrites of the 200 neurons in the network with the voltage amplitude indicated in color as a function of time. The plot shows that the event was initiated at cell # 35 (black arrow) and could propagate on either side of the network. (e) Transmembrane potentials at dendritic compartments (Vmd) and at the soma (Vms) for three cells (#50, 100, and 150) as a function of time show that the dendrites could generate a full and long-lasting action potential similar to an NMDA spike whereas the soma membrane experience only low level depolarization.
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a Cell 50 b 38.4ms 20.4ms Cell 100 10mV 10mV Cell 150 50ms 50ms
c d Cell 100 Cell 101 10mV Cell 102 50ms Cell 103 Cell 104 (mV) Cell 105
-20
-30
-40 10 mV
-50 50 ms -60 Stimulation on Stimulation off
Figure 4.10: Slow periodic activity propagation can be blocked by an anti-field in silico
Anti-field with waveforms identical to the propagating events were applied in a direction parallel to the dendritic axis using a current stimulator with a stimulus electrode near the cell # 100 (indicated by black arrow). The proportional current with opposite polarity was applied with a variable negative gain (K) to cancel the extracellular electric fields. The intracellular spike propagation using three different K (0, -0.006, and -0.018) were shown in (a-c). These results show that the propagation of the slow periodic activity was inhibited by the increase of an “anti” field. The intracellular potentials recorded in three cells (#50,
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100, and 150) show an increased delay, and even propagation stopped when K increased to -0.018. (d) The intracellular membrane potentials of the cells near the stimulation electrode (cell # 100~105) show that the applied anti-field can block the events without causing hyperpolarization.
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a c
b
d Electrical artifact e REC1 NS
Triggered wave
REC2 Speed Speed (m/s)
100 ms 2+ Electrical
0.2 0.2 mV half Mg / half Ca2+ triggered wave
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Figure 4.11: Slow periodic activity propagation can be antagonized or stimulated by
electric fields in vitro
(a) Experimental setup of the extracellular electric field clamp. An amplifier records the local electric field, and a proportional controller generates an electrical field in a direction perpendicular to the dendrites capable of canceling the electric field of the propagating event (see Chapter 1 for additional details. (b) Electric field recordings obtained at three locations within the slice (proximal in black), at the site of the field application (red) and the distal site (green) show the local field potential in electrode 2 (red trace) was clamped to zero and that no slow hippocampal periodic activity reached the electrode 3 (green trace) when the clamping system was stimulation was turned on. (c) The plot of the amplitudes of oscillation recorded at the three sites indicating that periodic activity was blocked at the site 2 and 3. **:p<0.01. NS: Not significant.
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Chapter 5: Summary and Future Directions
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5.1 Summary
The main goal of this dissertation was to test the main hypothesis that neuro- electrical fields are not just passive reflections of underlying neural activity but can play an active role in shaping neural signals. The work presented in this dissertation used previously validated in silico modeling to test the feasibility of endogenous electric fields influencing self-propagation which was then followed by novel in vitro and in vivo electrophysiology techniques to experimentally show that electric field coupling mediates self-propagating, non-synaptic pathological and physiological waves in the hippocampus.
The objectives of this research were: (1) to determine if epileptiform waves self- propagate in the hippocampus by electric field coupling, (2) to determine if spontaneous waves can recruit neurons via electric fields across a physical cut, and (3) to determine if hippocampal waves under physiological conditions can also self-propagate non- synaptically by electric field coupling. The realization and summary of the results of these objectives are summarized in the following sections. Future directions from the implications of this dissertation will be discussed with preliminary experiments discussed.
5.1.1 Objective 1: To determine if epileptiform waves self-propagate in the hippocampus by electric field coupling.
Previous studies showed that 4-AP-induced spontaneous epileptiform waves traveling at 0.1 m/sec in the hippocampus are independent of synaptic transmission, gap junctions, or diffusion (12). Subsequent computational modeling studies showed that epileptiform waves traveling at ~0.1 m/sec could feasibly be mediated by electric field
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coupling (34, 106). Using these results, we carried out a series of experiments to determine if electric field coupling could mediate self-propagating epileptiform waves.
First, computer simulations predicted that the speed of propagation is dependent on the distance between neurons. To observe this effect in hippocampal tissue, we hypothesized that changing the osmolarity of the extracellular space would increase or decrease the propagation speed of 4-AP-induced waves traveling in the longitudinal axis of the hippocampus. We observed that 4-AP-induced epileptiform activity travelled significantly faster when extracellular osmolarity was lowered (cells swelling), and conversely travelled significantly slower when extracellular osmolarity was increased
(with the addition of mannitol, which dehydrates and shrinks the cells). The one limitation of this experiment was that we were unable to measure directly the size of the extracellular space to measure the relationship between the field and the propagation speed. However, these results are consistent with osmolarity and propagation speeds of other models of epilepsy (116).
Second, if endogenous electric fields mediate epileptiform wave propagation, then an anti-field of equal strength applied in the path of propagation should should block propagation. To test this prediction, we designed and validated a novel extracellular electric field clamp (EEFC) system that could affect only the extracellular electric field and not membrane polarization. The EEFC was derived from the commonly used intracellular voltage clamp technique so that an electric field can be clamped to zero at a specific location. When applied to spontaneous epileptiform waves, the EEFC system completely blocked transmission by cancelling the incoming endogenous field. This experiment
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provided clear indications that endogenous fields are required for the propagation of epileptiform activity.
We then investigated another method for decreasing the effect of extracellular electric field without affecting membrane polarization. Using a completely passive, high conductance array, we were able to decrease the amplitude and speed of propagation when the array was inserted into the tissue. It is important to note that the array did not completely eliminate the propagation due to two possible reasons: 1) the spatial extent of the field is much larger than the array, and 2) the array cannot generate a true short circuit between neural sinks and sources producing the electric field since the interface between the metal and ionic solution is best modeled as a capacitor, thereby increasing the bulk conductivity of the tissue (decreases the amplitude of the fields).
Finally, to investigate if these waves are self-propagating by electric field coupling, we theorized that for waves to self-propagate, endogenous fields must be able to activate neurons. We hypothesized that an initiated wave stimulated by an electric field of endogenous field strength will travel at the same speed as spontaneous epileptiform activity. We used a lower concentration of 4-AP to keep the hippocampal slice from generating spontaneous epileptiform waves but just excitable enough that when stimulated with a field of 5 mV/mm, we triggered a self-propagating wave.
For this objective, we hypothesized that spontaneous epileptiform waves can self-propagate by electric field coupling. Therefore, based on the above experimental results, we can conclude that epileptiform waves self-propagate in the hippocampus by electric field coupling
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5.1.2 Objective 2: To determine if spontaneous waves can recruit neurons via electric fields across a physical cut
Overall, the above experiments provided clear evidence that spontaneous epileptiform waves self-propagate by a mechanism consistent with electric field coupling.
However, it is unclear if electric fields are the sole mechanism driving non-synaptic 4-AP waves. In addition, we wanted to know if waves can be sustained by a self-excitatory loop via electric field coupling. We hypothesized that by propagating through a physical cut, spontaneous self-propagating epileptiform waves are non-synaptic and purely mediated by electric field coupling. Using computational modeling and acute in vitro/in vivo experiments, we set out to study the cellular and system level mechanism of endogenous electric fields.
First, we determined if spontaneous epileptiform waves can propagate through a physical cut. Making a cut not only modifies the extracellular space, it eliminates synaptic transmission and other forms of cell-to-cell communication. We hypothesized that since electric fields propagate through volume conductors, then waves mediated by electric field coupling should propagate through a cut. In both acute in vivo hippocampus and in vitro hippocampal slices, we observed spontaneous epileptiform waves propagating through a physical cut. An analysis of the propagation speed showed no significant difference regardless if a cut was present or not present, which suggest the waves are going directly through the cut and not around the cut. Furthermore, in the acute in vivo experiments, the amplitude of the waves decreased significantly after the cut was made, spatially, suggesting waves were self-propagating solely by electric fields.
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Finally, we provide experimental evidence showing that spontaneous epileptiform waves induced by 4-AP in the hippocampus generate electric field amplitudes in the physiological range of 2-6 mV/mm and are self-sustaining through a physical cut. This shows that via electric field coupling, weak endogenous electric fields proximal to the cut can influence and recruit a wave on the distal side of the cut. This data suggests that the amplitudes of endogenous electric fields are sufficient to not only modulate neural activity but act as the sole mechanism for exciting neural activity across a cut.
The findings from this study confirmed our hypothesis that self-propagating epileptiform waves are non-synaptic and purely mediated by electric field coupling.
5.1.3 Objective 3: To determine if hippocampal waves under physiological conditions can self-propagate, non-synaptically by electric field coupling.
To begin to study the functional relevance of the electric field coupling mechanism in the brain, we studied slow oscillation, or slow periodic, sleep waves that propagate in the hippocampus at approximately 0.1 m/sec. We hypothesized that slow oscillation sleep waves self-propagate non-synaptically in the hippocampus by electric field coupling. In this study, we showed both by blocking synapses chemically and observing propagation through a cut, that slow oscillation sleep waves are non-synaptic. We then tested the sensitivity of the propagation of slow oscillation waves to fast chemical (AMPA and GABAa) and electrical (gap junction) neurotransmission. Our results showed that the three respective blockers reduced the amplitude and the firing frequency but did not affect the speed of propagation. We then tested for NMDA sensitivity and found that application
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of APV (NMDA antagonist) blocked the propagation of slow oscillation waves, suggesting sleep waves are NMDA-dependent.
To determine the feasibility of electric field coupling mediating slow oscillation activity, we applied in silico modeling and in vitro experiments as previously discussed in the above two objectives. Computational modeling established that electric field coupling can mediate slow oscillation waves traveling in the hippocampal network. Experimentally, we first determined if modifying the extracellular space would affect the periodic activity.
We observed a significant decrease in propagation speed when applying the diuretic furosemide to increase the extracellular space. We then blocked propagation with the EEFC and triggered a self-propagating wave by electric field stimulation to show that endogenous electric fields are involved in generating self-propagating slow oscillation sleep waves in the hippocampus. The findings from this study confirmed our hypothesis that slow sleep waves self-propagate non-synaptically by electric field coupling.
This thesis work has shown that synaptic transmission is not the only dominate mechanism of neural communication. Under both pathological and physiological conditions, hippocampal waves excite and recruit neurons non-synaptically by endogenous self-sustaining electric fields. These NMDA-sensitive hippocampal waves can be influenced by modifying the extracellular space and extracellular electric field, providing clear experimental evidence that electric field coupling is the sole driving mechanism behind self-propagating, non-synaptic waves.
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5.2 Significance
Through in vitro and in vivo electrophysiology studies, we defined and characterized a new mechanism of propagation of neural activity in the brain. The ~0.1 m/sec propagating speed was observed under both pathological and physiological conditions that led us to investigate a common mechanism that could explain how waves travel and recruit neurons in the brain. While synaptic transmission plays a significant role in transmitting information, we believe electric field coupling is a significant secondary non-synaptic mechanism that can complement neural excitation needing either synapses or electric field coupling, or both mechanisms. The results presented in this thesis indicated that endogenous electric fields are capable of mediating propagation of self-regenerating neural activity, a concept not well investigated in the neuroscience community. This line of research could help explain many basic physiological functions such as memory consolidation or clearing of memory to form new memories (19, 165, 166). In pathological conditions, we have shown that non-synaptic epilepsy can be detected and controlled by targeting electric fields mediating the generation and recruitment of neurons. For the neuromodulation community, endogenous electric fields could be the neuronal response that could explain many long-lasting therapeutic effects from stimulating the brain via DBS or non-invasive tDCS or TMS to treat Parkinson’s, epilepsy, or neuropsychiatric diseases(58, 154, 191–193). Of course, the results presented here are only scratching the surface of the significant implications of self-propagating waves by electric field coupling can have on both pathological and physiological brain functions, and further studies need to be designed and investigated to see a significant push in the field of electric field coupling. 143
5.3 Future Directions
This thesis laid a strong experimental foundation for studying ephaptic coupling as a propagation mechanism that can be a new target for treating pathological brain diseases such as epilepsy. Both modifying the extracellular space and applying the EEFC system have the potential to be adapted in the clinical setting as new therapies to target non- synaptic epilepsy. In fact, diuretics such as furosemide and bumetanide have already been studied pre-clinically to treat focal epilepsy (150, 151, 194). The EEFC system has the potential to be used as the first true closed-loop brain stimulator that targets endogenous fields around seizure focus to prevent spread/generalization of the seizure or even block the seizure all together. Immediate studies would be to measure the endogenous electric field in an acute or chronic focal epilepsy model and then apply an anti field of equal strength via an open-loop or closed-loop (like the EEFC system) to see if we can block the generation or spread of the seizure.
Another future direction would be to use our current understanding of electric field coupling and determine if the effects of non-invasive neuromodulation techniques such as tDCS or tACS can be explained by endogenous electric field coupling. A study could be established to investigate if we can antagonize or enhance electric field coupling using non- invasive tDCS or tACS and determine what happens functionally when the endogenous fields are targeted. Ultimately, tDCS could be potentially utilized to target endogenous electric fields to treat pathological diseases, such as epilepsy, or under physiological conditions, to enhance memory.
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Understanding the role of electric field coupling in normal physiology will be important in understanding how the brain functions. A future study to consider is using the novel non-synaptic in vivo preparation (transection/cut) and carrying out chronic experiments to study self-propagating, non-synaptic waves by electric field coupling under physiological (sleep, memory consolidation/clearing) conditions or during different stages of brain development. These studies will be critical in determining a concrete functional relevance to ephaptic, or electric field coupling in the brain.
Another study would be to investigate the feasibility of injecting a non-conductive, bio-compatible material in the cut/transection to isolate a seizure focus and prevent the spread of epilepsy in non-diseased tissue. This technique could improve current surgical transection treatment techniques and could minimize or improve the side-effects that make epilepsy a social burden. In a preliminary study, we 3-D printed an in vitro tissue holder that can electrically isolate two halves of the recording chamber (see in Appendix Fig.
A2.1). Each side receives its own ionic aCSF line with no mixing between halves. In the middle, there is the capability of inserting a non-conductive material such as a glass wall
(we used a glass coverslip with 140 µm thickness). The hippocampal slice was first placed in one half of the chamber so that the entire tissue could be bathed in the same 4-AP aCSF solution. A cut (<200 µm) was made and propagation across the cut was observed (Fig.
A2.2A). We then transferred one half of the slice to the other half of the chamber that was electrically independent, and inserted a glass cover slide within the cut. When the nonconductive glass was inserted, activity remained on the temporal half of the slice but immediately stopped appearing on the septal half (Fig. A2.2B). This very preliminary study
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suggests non-conductive materials can be used to block non-synaptic propagation without chemically altering the tissue that could have altered consequences for other brain functions.
Finally, we have observed that waves between 100-200 msec pulse width propagate by electric field coupling. It may be interesting to study the actual characteristics of the wave (pulse width, pulse amplitude, spiking frequency, power, etc.) to see if there is relationship between the actual waveform and the endogenous electric field that can be used for calculating a threshold of activation by electric fields.
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Appendix
A1: Computational Model of Electric Field Coupled Hippocampal Network
developed by Xile Wei, PhD (Professor of Electrical Engineering and Computer
Science, Tianjin University, China)
Modified with permission from Journal of Physiology, 2019, Vol. 597, Issue 1 January 2019, pp. 249-269; Copyright© John Wiley and Sons Publishing Slow periodic activity in the longitudinal hippocampal slice can self-propagate non- synaptically by mechanism consistent with ephaptic coupling Chia-Chu Chiang*, Rajat S. Shivacharan*, Xile Wei*, Luis E. Gonzalez-Reyes and Dominique M. Durand *These authors contributed equally
A2: A 3D printed 2-compartment electrically isolated in vitro slice chamber design and preliminary results completely blocking hippocampal wave propagation across
a cut.
147
A1. Computational Model of Electric Field Coupled Hippocampal Network developed by Xile Wei, PhD (Professor of Electrical Engineering and Computer
Science, Tianjin University, China)
Hippocampal neural network.
The computational neural network model was modified based on our previous study to capture the features of NMDA-dependent spiking propagation in the cellular layer in the hippocampus (34). The hippocampal network in the cell layer region was set with the dimensions 3728μm(X)×336μm(Y)×360μm(Z) (Fig. A1.1a), where X and Z are represented as the longitudinal and transverse directions of hippocampus respectively, and
Y is the tissue thickness along the cellular axial direction. The network of this region is made up of cell arrays with 200 cells in the x-axis and 18 cells in the Z axis (Fig. A1.1b).
The center distance between two adjacent cells was 18.64μm, and the cell edge-to-edge distance dcc ranged between 0.84 and 2.84μm (Fig. A1.1c). The values of dcc are assigned to the different values under different conditions (Table A1.1). To simulate the cell density throughout the depth of a tissue slice, a “stacking factor” (SF) is used to take into account the actual number of cells around one stack network (Fig. A1.1d). Here, the value of SF is in the range between 10 and 30 (106).
Single cell model.
Each cell only contains one compartment for soma and another compartment for the dendrite. This two-compartmental model (Fig. A1.1e-f) for a CA1 hippocampal pyramidal cell (HPC) was built using Matlab simulation environment. This model was
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tested for half-Ca2+/half-Mg2+ aCSF-induced hippocampal slow periodic activity. In the model, the center distance of adjacent cells is set constant with a value of 18.64μm (195).
2+ To mimic the effect of extracellular calcium concentration [Ca ]o on the hippocampal
2+ network activities, the cell diameter is used as the substitute parameter for [Ca ]o because
2+ the decreased [Ca ]o induces cell swelling. Similar as to the previous model(195), the cell diameter under the low-Ca2+ condition is 17.8μm with the distance between each two adjacent neurons dcc=0.84μm (Table A1.1 and Fig. A1.1c). The previous experiments
(196, 197) showed that the extracellular resistance in a low-Ca2+ environment increased
2.5~3-fold compared to the standard physiological solution. Based on the relationship between extracellular space and tissue resistance, the cell diameter under the normal Ca2+ condition has a value of ~15.8μm with dcc=2.84μm (Table A1.1 and Fig. A1.1c) which is within the physiologic range from 2 to 4μm. The volume ratio change 푟푉 (see definition in
2+ Table A1.1) is proportional to [Ca ]o change in a linear interpolation. Thus, the cell
2+ diameter under the half-Ca condition is set about 16.8μm with dcc=1.84μm in this model
(Table A1.1 and Fig. A1.1c). The connected section between somatic and dendritic compartments has a length of 250μm with the diameter of 4.9μm. The passive membrane parameters are set to the following values (198): somatic membrane resistance 푅푚푠 =
2 2 680 훺 ∙ 푐푚 , dendritic membrane resistance 푅푚푑 = 34200 훺 ∙ 푐푚 and membrane
2 capacitance 퐶푚 = 1.0 휇퐹/푐푚 ; for both somatic and dendritic compartments, and axial resistance 푅푖 = 530 훺 ∙ 푐푚. With these parameters, the electronic parameters for each compartment can be determined by cable theory, listed in Table A1.2.
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NMDA receptors are widely distributed in dendrites including both synapses and extra-synaptic regions (36), and therefore NMDA receptor channels are included in a dendritic compartment in the model. In addition, the dendritic compartment contains a delayed rectifier potassium current 퐼퐾퐷푅. The somatic compartment is considered as a passive compartment without any active channel since this model is designed to test the hypothesis that NMDA-dependent spikes observed in vitro can propagate in silico.
The transmembrane potentials (푉푚_푑, and 푉푚_푠 ) for two compartments of the model are described by the relationship
푑푉푚_푑 푔푐_푠푑 퐶푚 = −퐼푁푀퐷퐴 − 퐼퐾퐷푅 − 퐼퐿_푑 − (푉푚_푑 − 푉푚_푠) (1) 푑푡 퐴푑
푑푉푚_푠 푔푐_푠푑 퐶푚 = −퐼퐿_푠 − (푉푚_푠 − 푉푚_푑) (2) 푑푡 퐴푠
The gating equations for each active current in dendrite were implemented using the
Hodgkin-Huxley formalism as in Table 3. The channel conductances are 푔푁푀퐷퐴̅ =
2 2 4.43ms/푐푚 , and 푔퐾퐷푅 = 67ms/푐푚 . The reversal potentials are 퐸푁푀퐷퐴 = 0푚푉, 퐸퐾 =
−60푚푉, 퐸퐿_푑 = −58푚푉, and 퐸퐿_푠 = −58푚푉.
The dynamics of gate variable 푞 for 퐼퐾퐷푅 in dendrite is described by
푑푛 = 훼 (푉 ) − 푛 ∙ (훼 (푉 ) + 훽 (푉 )) (3) 푑푡 푛 푚_푑 푛 푚_푑 푛 푚_푑 with the variable rate functions
150
0.00049∙(푉푚_푑−32) 0.00008∙(푉푚_푑−42.0) 훼푛 = 푉 −32 , 훽푛 = 푉 −42.0 (4) 1.0−푒푥푝(− 푚_푑 ) 푒푥푝( 푚_푑 )−1.0 25.0 10.0
In the case of the NMDA-gated channel, there is a marked voltage-dependency in the presence of extracellular magnesium. For physiological magnesium concentrations, the dependence on the voltage of NMDA receptor-mediated current 퐼푁푀퐷퐴 can be integrated
in a gating function 퐵(푉푚푏푑 ) that multiplies the NMDA conductance 푔푁푀퐷퐴̅ (Table A1.3).
This gating function is
1 퐵(푉 ) = 2+ (5) 푚_푑 [푀푔 ]표 1+ exp (−푘퐵∙푉푚_푑) 푀0
2+ 2+ where [푀푔 ]표 is the extracellular 푀푔 concentration (units: mM) with a value of 2mM
2+ in normal ASCF and 푀0and 푘퐵 are constants shown in Table A1.3. Half-Mg condition
2+ are considered and thus [푀푔 ]표 has a constant value of 1mM. It should be noted that
푔푁푀퐷퐴̅ in this model is proportional to fraction of NMDA channels in the open state 푂푁푀퐷퐴 and the kinetics of 푂푁푀퐷퐴 depends on the glutamate level in the extracellular space around those NMDA receptors.
Electric field coupling.
To test the hypothesis that endogenous electric field alone could induce NMDA- dependent neural propagation observed in vitro, the communication between adjacent cells is limited to bidirectionally electric field coupling and restricted to the longitude direction
(X-axis). The electric field effect is calculated using the quasi-static formulation of the
Maxwell equations assuming homogeneous and linear volume conductors. According to
151
Ohm’s law, the corresponding potential 휑 at the point P at a distance relative to the reference electrode in a medium of resistivity 휌 is described as follow:
휌 휑 = ∙ 퐼 (6) 4휋푟
Eq. (1) can be applied to monopolar electrodes from each of two compartments from a source Cell(i, j) in the network array with transmembrane currents 퐼푖,푗_푡푟푎푛_푑, and 퐼푖,푗_푡푟푎푛_푠 at the corresponding distances to each of two compartments of the target Cell(k, l) (푗 ≠ 푙) in the cell array. The extracellular potential at two compartments of the target Cell(k, l) is given by the following:
휌 퐼(푖,푗)_푡푟푎푛_푑 퐼(푖,푗)_푡푟푎푛_푠 푉(푘,푙)_푒_푧 = 푆퐹 ∙ ∑(푖,푗) ( + ) (푧 = 푑, 푠) (7) 4휋 푟(푖,푗)_푑→(푘,푙)_푧 푟(푖,푗)_푠→(푘,푙)_푧
where SF is the stacking factor, 푉(푘,푙)_푒_푧 is the extracellular potential inserted at target compartment z of the target Cell(k, l) , 퐼(푖,푗)_푡푟푎푛_푧 is the transmembrane current of two compartments in source Cell(i, j) located at distances 푟(푖,푗)_푑→(푘,푙)_푧 and 푟(푖,푗)_푠→(푘,푙)_푧 from the target compartment z (Fig. A1.1f), and 휌 is the extracellular resistivity with the range of 250~380 훺 ∙ 푐푚 (199, 200).
Extracellular potential, field amplitude, and speed measurement.
To measure the extracellular potential and electric field, we placed 2×3 virtual multi-electrode array outside of the network paralleling to (X, Y) plane (Fig. A1.1g). The virtual electrode array was placed about 30μm away from the surface layer of the rectangular cell array to account for approximately three rows of the dead cell around the inserted electrode. All extracellular potential at the virtual electrode array and the electric 152
field were calculated by calculating the spatial derivatives of extracellular potentials along the y-axis. The propagation speed was measured based on the three extracellular recording at the top of the virtual electrode array where peak times of the events were recorded, and the delay from either two virtual electrodes. The propagation speed was derived by taking the traveling distance dividing by the delay time. To initiate the spontaneous slow periodic activity observed in vitro experiments, stochastic noise inputs (mean ± std: 0 ± 0.3μA/cm2) were inserted into both dendritic and somatic compartments.
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A1. Figures and Tables
a e f
INMDA Cell (i, j) Cell (k, l) Y Z 푉(푘,푙)_푒_푑 Dendrite X IKDR Dendrite X: Longitudinal Z: Transverse ILeak Y: somatic-to-apical dendritic 18 cells Y 200 cells b d I X ( 200 cells, 4000μm) Leak Soma Soma T S
) 푉(푘,푙)_푒_푠 μm
g
dc-c Z (18 cells, 360cells, (18Z dc-c Mt V Y e_Mt c X 125μm
Z Mb Ve_Mb Rout Y 30μm Z RCell
d c-c Figure A1.1: Model of Hippocampal Network
(a) 3-D view of one stack comprised of 200×18 pyramidal cells whose somas were in xz plane. The simulated region is approximately by 3700μm(X)×320μm(Y) )×360μm(Z). The red rectangle represented one somatic plane layer. (b) Top view in (X, Y) plane (solid- colored circles represent soma position). (c) The definitions of the soma diameter, the cell radius (Rcell), the constant outer diameter of each sphere (Rout), and the soma edge-to-edge distance (dcc). (d) The physical representation of the stacking factor (SF). White-colored cells represent the actual modeled cell location, whereas gray-colored cells represent the virtually stacked cells around the modeled cell locations. (e) Each modeled cell contained two compartments: dendrite and soma. Three ion channel currents (INMDA, IKDR, ILeak) are added to the dendritic compartment. The somatic compartment is considered as a passive compartment. Cell(i,j) and Cell(k, l) represented any two cells of the network in a different column (Z axis) in xz plane, where 1≤i,k≤200, 1≤j,l≤18, and j≠l. Electric field couplings
154
between any two compartments among Cell(i,j) and Cell(k, l) were bidirectional. (f)
Extracellular potentials (V(k,l)_e_d, and V(k,l)_e_s) acted on each extracellular node of two compartments of the target Cell(k, l) using Eq. (2). Field effect on each compartment of the target Cell(k, l) is the superposition of all fields generated by all source Cell(i,j). (g) A virtual 2×3 multi-electrode array (MEA) is mimicked to match the recording electrodes of in vitro experimental settings. This MEA is placed parallel to and 30μm away from the surface layer in xy plane of the network. The solid black circles are virtual recording electrodes on the top (Mt) and the bottom (Mb). The bottom electrodes are placed in the same plane as the somatic layer.
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Table A1.1: Parameters under conditions with 3 different calcium concentrations
Parameter Normal Ca2+ Half Ca2+ Low Ca2+ condition (2mM) condition (1mM) condition (0.2mM) Cell diameter 15.8μm 16.8μm 17.8μm 퐷푐푒푙푙 Cell spacing dcc 2.84μm 1.84μm 0.84μm (*)Volume ratio 0.63 0.36 0.15 푟푉 (*): Volume ratio 푟푉 can be described as 4휋푅3 4휋푅3 4휋푅3 푟 = [ 표푢푡 − 푐푒푙푙]⁄ 푐푒푙푙 푉 3 3 3
Table A1.2: Circuit parameters in computational model
Parameter symbol Value Somatic membrane 푅 680 훺 ∙ 푐푚2 resistance 푚푠 Dendritic membrane 푅 34200 훺 ∙ 푐푚2 resistance 푚푑 2 Membrane capacitance 퐶푚 1.0 휇퐹/푐푚 axial resistance 푅푖 530 훺 ∙ 푐푚 Conductance between soma 푔 1.43 × 10−5 푚푠 and apical dendrite 푐_푑푠 Membrane leakage 푔 1.47 푚푠/푐푚2 conductance for soma 푚푠_퐿푒푎푘 Membrane leakage 푔 0.029 푚푠/푐푚2 conductance for dendrite 푚푠_퐿푒푎푘
Table A1.3: Hodgkin-Huxley equations of different channels in the model
Channel Gating functions
퐼푁푀퐷퐴 푔푁푀퐷퐴̅ ∙ 퐵(푉푚_푑) ∙ (푉푚_푑 − 퐸푁푀퐷퐴) 4 퐼퐾퐷푅 푔퐾퐷푅 ∙ 푛 ∙ (푉푚_푑 − 퐸퐾) 퐼퐿_푑 푔푚푑_퐿푒푎푘 ∙ (푉푚_푑 − 퐸퐿_푑) 퐼퐿_푠 푔푚푠_퐿푒푎푘 ∙ (푉푚_푠 − 퐸퐿_푠)
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A2. A 3D printed 2-compartment electrically isolated in vitro slice chamber design and preliminary results completely blocking hippocampal wave propagation across a cut.
Figure A2.1: Design and implementation of 3D printed 2-compartment electrically
isolated in vitro slice chamber
(A) Rendering of the 3D printed 2 compartment chamber. Designed in Solidworks and printed on Object 350 Connex3 Polyjet 3D printer with ABS material. (B) Integration of
3D printed chamber in current in vitro electrophysiology rig. Chamber was glued to the rig using silicone.
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Figure A2.2: Blocking spontaneous epileptiform wave through a cut
(A) 4-AP aCSF solution flows perpendicular to propagation direction. Spontaneous epileptiform waves propagating across a cut from REC1 to REC2. (B) Each half of the tissue slice was place in electrically isolated chambers. Activity continued in REC1, but was unable to cross when glass wall was added.
158
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