Final report for Research Internship 1 (25 EC) of the
Master Brain & Cognitive Sciences
A N A LY S I S O F N E O C O R T I C A L N E U R A L A C T I V I T Y C O R R E L AT E S O F H I P P O C A M PA L T H E TA R H Y T H M by siavash ahmadi under Francesco P. Battaglia
Institute for Interdisciplinary Studies Faculty of Science
Siavash Ahmadi: Analysis of neocortical neural activity correlates of hippocampal theta rhythm, © July 2012
A B S T R A C T
The brain is a highly modular organism capable of performing local as well as global integration of information via distinct neuronal circuitry, transforming sensory input into appropriate behavioral motor output through the employ-ment of recurrent and feedforward networks responsible for the manipulation of information in form of online and retrograde (i.e. stored associational) infor-mation processing. The brain, however, has to handle the raw data it gets from the input organs with biologically founded solutions, the key to this challeng-ing prospect bechalleng-ing the ability to transmit data effectively. Many lines of research have looked into this faculty of biological brain networks in order to gain insight into the mechanisms of information transfer among neurons. A major success in this path is reflected in the large body of evidence corroborating a role for the oscillatory brain neuordynamics—regular and coordinated rhythmicity in form of fluctuating neuronal firing and transmembrane electric potentials, exhibiting a periodic pattern at different frequencies.
A relatively narrow frequency band in which such dynamics occur in the brain is the theta band, involved in many cognitive domains, including spa-tial navigation and memory which we consider here, with compelling evidence bolstering its importance and widespread deployment. Subcortical regions es-pecially the hippocampus and the associated areas, are the original locus of the theta signal. Current literature entails that the role of the hippocampus and its oscillatory mechanisms cannot be overstated in mediating communicative goals, becoming in close contact with the neocortical populations via oscillatory channels that influence a wide range of the brain.
However, despite great interest in the field, lines of investigation have failed to address the global picture of the impact of hippocampal neuronal activity on the distinct areas of the neocortex. Here, through an exploratory approach, with the primary goal of constructing a cartographic representation of modula-tory hippocampal influences on the neocortical networks in the brain of rodent, we utilize several statistical and spectral analysis approaches to analyze a fairly large database of raw data recorded from the rat brain. We strive to character-ize specific effects building upon previous research and further report a novel coherency with the theta second harmonic observed within a major fraction of neocortex of the rat. The implications of the current research would be the designation of the potential involvement of the hippocampus as a coordinator module within the brain.
P R E FA C E
This work was carried out in a period of almost five months from February
through July 2012. Formally, as a 25 EC1 internship, this project required me to
devote at least four months to full-time work and present the results in form of a report. After five months of challenging full-time work, I found the results comprehensive enough to be reported, although as is always the case more work could still be done on the data. Hence, in the future, I will hopefully continue to look into the data sets even more thoroughly and hopefully get new insights into the possible interesting clues present in the data.
As I did my bachelor’s degree in computer science and I got interested in the fascinating realm of the science of brain, I decided to pursue a research career in the neurosciences. This transition, however, was tough as I have had to work re-ally hard to make up for my lack of adequate knoweldge in neurobiology when I first entered this field and the build-up of this required knowledge proved to be very challenging. I am aware that students of computer science, mathemat-ics and physmathemat-ics are becoming increasingly enticed by the neurosciences and a surge of talents is finding its way into the field. I understand the difficulties that such a group of students may face, ergo in preparing this report, I have tried to make it as much self-contained and accessible as possible, both for it to be easy to read by others, and to summarize what I have used or learned in a compact form. Also, I am aware that the material I am presenting here might not be astoundingly exceptional as this project is my very first endeavor in the neurosciences towards a heavily research oriented future career.
Four appendices are included that breifly describe the mathematical back-ground of the tools employed in the analyses, along with the more complete set of results obtained that due to lack of space were not accomodated in the main text. Inspired by other good templates in books and journals, one of my goals in choosing this specific template has been to exploit the blank space on the margins of each page to explain the technical terms briefly.
In the course of the project I have used MATLAB scripts previously written by
my Supervisor and also computational toolboxes such as Chronux (Bokil et al.,
2010) and FieldTrip (Oostenveld et al., 2011). I have also written some custom
scripts which are indeed available upon request.
1 European Credits
The organization of the document is as follows. In the first chapter, a review of the relevant literature is presented. Second chapter offers the results of the analyses. Discussion of the results follows in the next chapter, before I go into the description of the data collection and the analyses performed in chapter four. Ultimately, the appendices comprising the mathematical and neuroscien-tific background as well as the full set of maps show up in the second part.
My best friend gave me the best advice He said each day’s a gift and not a given right Leave no stone unturned, leave your fears behind And try to take the path less traveled by That first step you take is the longest stride —Nickelback
A C K N O W L E D G M E N T S
There is always too many people to thank using only little amounts of paper. In
fact, I believe one could thank all the bits and pieces one encounters in their life1.
Nontheless, I wish to explicitly acknowledge those who were directly involved in my project and whose support aided me get through it.
First, I thank Francesco Battaglia, my supervisor, who accepted me as a stu-dent and also insisted that I do not get my hands dirty doing experiments in such a short period of time. Only now do I understand why he said so! Francesco was a great guy, and although very busy, always tried to help me out. Francesco, I think the most important lesson I learned from you was that I need to learn a lot lot more. Thank you for all the support and making me realize this.
I would like to thank Conrado Bosman who helped me with discussions and things he taught me. I also thank Martin Vinck who especially in the final stages of this project gave me nice suggestions and advice regarding the technicalities involved in spectral analysis.
A big thanks goes to André Miede for this super awesome LATEX template.
Thank you very much for your work and the contributions to the original style.
There is a LYX port of this template available as well which I used at one point2
to typeset the document. However, I switched back to LATEX in the end. The LYX
port of the template was initially done by Nicholas Mariette in March 2009 and continued by Ivo Pletikosi´c in 2011. I also thank the Open Source Community at large who are working hard to make their peers’ lives easier and more joyful.
Finally, I am inexpressibly grateful to my uncle, Aidyn, who has always sup-ported me especially along the way with my studies and financial matters in Amsterdam. Without his help, I would never have been able to have the oppor-tunity to capitalize on my energy so early in my life and so rapidly as well.
1 Several philosophical books could be written on the reason why.
2 One of those times when all the disasters in your computer accumulate to unveil at the time of need.
C O N T E N T S abstract v preface vii acknowledgments ix The Report 1 1
introduction
3 1.1 Anatomical background 41.1.1 The hippocampal region 4
1.1.2 Neocortex 6
1.2 Role of the hippocampus 7
1.2.1 Spatial navigation 7
1.2.2 Memory consolidation and retrieval 8
1.3 LFP oscillations, phase-locking and temporal referencing 9
1.4 Communication within and beyond HC-PFC circuitry 11
2
results
132.1 Theta modulation across neocortical sites 13
2.1.1 Time dependent theta modulation 14
2.1.2 Bimodal modulation 16
2.1.3 Using the PPC measure to confirm modulation 17
2.2 Coherency detection using spectral analysis 18
2.3 Spectral analysis reveals uniform second-harmonic locking of
neo-cortical neurons 19 3
discussion
23 4methods
29 4.1 Data acquisition 29 4.1.1 Experimental setup 29 4.1.2 Electrophysiological recordings 29 4.2 Analyses 304.2.1 Spike phase distribution 30
4.2.2 Global coherograms 31
4.2.3 Autocorrelograms 31
Appendix 33
a circular statistics 35
a.1 Simple summary statistics 35
a.2 Parameter estimation 37
a.3 Pairwise Phase Consistency 37
a.4 Hypothesis testing 37
xii contents
a.5 Data display 38
b spectral analysis 39
b.1 The Fourier transform 39
b.2 Spectral estimation 40 b.2.1 Multi-taper methods 40 b.3 Signal coherency 41 c modulation maps 43 d miscellaneous figures 77 References 79
L I S T O F F I G U R E S
Figure 1 Hippocampal formation 5
Figure 2 Relative modulation maps 14
Figure 3 Modulation level varies with time in a dilating window 15
Figure 4 Relative bimodal modulation maps 16
Figure 5 Bimodal modulation map 16
Figure 6 PPC vs. Rayleigh p-value 17
Figure 7 Coherogram of a sample cell reveals highly modulated
bouts of activity 18
Figure 8 Sample locked autocorrelogram 20
Figure 9 Differential yields of Hilbert transform and
autocorrelo-gram 20
Figure 10 Mean cross-frequency coherograms 21
Figure 11 Simple computational model 26
Figure 12 Simple computational model 26
Figure 13 Circular maze and recording array 30
Figure 14 Heuristic detects ‘bad’ signals 32
Figure 47 More autocorrelogram examples 77
Figure 48 Miscellaneous coherogram maps 78
L I S T O F TA B L E S
Table 1 Reading the modulation maps 43
xiv acronyms
A C R O N Y M S
LFP Local Field Pontential
HC Hippocampus
EC Entorhinal Cortex
DG Dentate Gyrus
1
I N T R O D U C T I O N
The brain is a highly modular organism capable of performing local as well as global integration of information via distinct neuronal circuitry, transforming sensory input into appropriate behavioral motor output through the employ-ment of recurrent and feedforward networks responsible for the manipulation of information depending on the internal state of the brain (with present desires, goals and prior memories alike). An example of such a local procedure would be computations at the systems level such as visual recognition of simple gabor patches versus the computations necessary to use the information from those recognized patterns in a perceptual decision making task to perform an action following the observation of certain visual stimuli, referred to here as “global.” The brain has to handle the raw data it gets from the input organs with biolog-ically founded solutions, the key to which is the ability to transmit data effec-tively. Many lines of research have looked into this faculty of biological brain networks in order to gain insight into the mechanisms of information transfer among neuronal circuits. A major success in this path is reflected in the large body of evidence corroborating a role for the oscillatory brain neuordynamics— regular and coordinated rhythmicity in form of fluctuating neuronal firing and transmembrane electric potentials, exhibiting a periodic pattern at different fre-quencies. Despite such progress, a detailed account of how the physiological mechanisms effectively carry out the task of information transfer is still lacking.
A relatively well-defined frequency band in which brain dynamics occur is the theta band, involved in many cognitive domains, including spatial naviga-tion and memory which we consider here, with compelling evidence bolstering its importance and widespread deployment. Subcortical regions especially the
Hippocampus (HC) and the associated areas (e.g. medial septum) are the original
locus of the theta signal. Current literature (to be discussed in depth through-out this chapter) entails that the role of the hippocampus and its oscillatory mechanisms cannot be overstated in mediating communicative goals, becoming in close contact with the neocortical populations via oscillatory channels that influence a wide range of the brain.
Despite great interest in the field, lines of investigation have failed to address the global picture of the impact of hippocampal neuronal activity on the dis-tinct areas of the neocortex. Here, through an exploratory approach, with the primary goal of constructing a cartographic representation of modulatory
4
introduction
ences of the hippocampal oscillations on the neocortical networks in the brain of rodent, we utilize several statistical and spectral analysis approaches to ana-lyze a fairly large database of raw data recorded from the rat brain. We strive to characterize specific effects building upon previous research and further report a novel coherency pattern with the theta second harmonic observed within a major portion of neocortex of the rat. The implications of the current research would be the designation of the potential involvement of the hippocampus as a coordinator module within the brain along with the quantified maps presented. Particularly, in this chapter, we review the relevant background literature, first providing the anatomical structure of the areas with which we are concerned in this study, discussing the respective functional and cognitive roles of those structures next, subsequently looking at the recent reports on communication in the brain and the role of the hippocampus in the entrainment of dynamics of local brain networks. In subsequent chapters, the results precede a discussion developed on the obtained results. A chapter is devoted to the description of methods, with four additional chapters annexed as Appendices, bearing the more detailed explanation of the mathematical methods of circular statistics and spectral analysis used in treating the data and the full maps.
1.1 anatomical background
In this section, we review the anatomical details of the hippocampal regions and the neocortex in an extremely abridged form. The bulk of the content in
this section is adapted fromWitter and Amaral(2004).
1.1.1 The hippocampal region
Although there is no consensus as what structures should be referred to by the term hippocampal region, it can be argued that one could divide it up into two distinct regions: hippocampal formation (comprising the dentate gyrus, hip-pocampus proper, and the subiculum), and parahippocampal area (comprising the entorhinal, perirhinal and postrhinal cortices). The disagreement on the def-inition of the term is due to the nonidentical criteria accepted by researchers. Essentially, the parahippocampal region is defined either by the connections within and between its relevant structures or by their anatomical characteristics such as the number of layers. The substrctures of the hippocampal formation are three-layered (formerly known as the allocortex) with their connections
be-Allocortex a formerly used term for
the hippocampal formation ing essentially unidirectional. Here, the hippocampus proper is further dividedinto three fields CA1, CA2, and CA3.
Spatially, the hippocampal region of the rat is part of the forebrain located underneath the corpus callosum, posterior to the septum, and is bent ventrally
and laterally with a concave curve as seen from the septum (Figure 1;Kjonigsen
et al.,2011). The axis passing through the hippocampal formation is called the
septotemporal axis. The hippocampal region is surrounded by the temporal and posterior lobes. The principal cell type of the hippocampus is the pyramidal cell. However, there exist subtle differences between the localized versions of
Pyramidal cell principle nerve cell type in several cortical regions including the hippocampus and neocortex resembling the shape of a pyramid
1.1 anatomical background 5
the pyramidal cells in different spots of CA1 and CA3, dividing the respective fields into finer areas.
Figure 1: HC Formation.
In particular, the CA1 region, which is characterized by a thin layer of densely packed pyramidal cells. CA1 is close to the medial septum, postulated to be the princi-pal intrinsic generator of rhythmically
oscil-lating local field potentials (see Section 1.3;
Buzsáki,2002). CA1 pyramidal cells receive
input from CA3 and layer III of the en-torhinal cortex (EC-III) and topographically project to subiculum, with some interneu-ron projections to CA3.
The terminology for the hippocampus proper currently in use in the literature is the legacy of the Spanish-American
neuro-physiologist (see the reference byWoolsey)
Rafael Lorente de Nó who devised the term Cornus Ammonis (or Ammon’s horn) to refer to the distinctly wired regions of the hippocampus. Initially, he defined region CA2 as a narrow band situated in between CA1 and CA3 with a cell morphology resembling that of the CA3 neurons, yet receiving no connections as those terminating at CA3 cells. Such a definition is however disputed and there is little agreement on area CA2 with the term appearing rarely in the literature on the functional aspects of the cell assemblies of the hippocampus.
Unlike CA1, CA3 is rich with recurrent connections. CA3 networks supply
part of the input to CA1 via Schaffer collaterals, with individual cells in this Schaffer Collaterals
axon collaterals (major branches) of the CA3 pyramidal cells named after Károly Schaffer
region generally more active than those in CA1 (Mizuseki et al., 2012). CA3
ouput ends at the CA1 cells, with no innervation of the EC or the subiculum or related parahippocampal regions (the pre- and parasubiculum). The projections from CA3 to CA1 are not uniform in that the topography of the connections is biased by the position of the projecting CA3 neuron giving rise to a gradient
distribution of the terminals. CA3 gets extensive input from the granular layer Granular Layer
layers in the cortex made up of granule cells which are called so because of their grainy look
of the Dentate Gyrus (DG) onto its pyramidal cell layer.
DGis a three-layered structure with the granule cell layer on the surface, the
molecular layer in the middle and the polymorphic laye deep inside. The gran-ule cell type is the principal neuronal type – ellipsoid-like neurons with typical
conic dendritic processes – within theDGand is denser near the septum than in
the more lateral parts. DGis located in the ventral portion of the hippocampus
and receives its major afferents from the Entorhinal Cortex (EC) with no direct Afferent
input to neurons
inputs from other cortical areas. DGprojects to the CA3 field of the
hippocam-pus.
The last structure within the hippocampal formation is the relatively under-investigated subiculum, a major subcortical output target of the hippocampal
neurons. In the parahippocampal area, theECprojects via the so-called perforant
6
introduction
EC verges on the hippocampal formation ventrally from the more caudal parts. The EC receives substantial output connections from the subiculum.
1.1.2 Neocortex
The neocortex (a.k.a. isocortex) is the phylogenetically youngest part of the
cor-Phylogenetics the study of the evolution of organisms and establishment of related taxonomic graphs
tex with a homogeneous six-layered organization. One possible division scheme of the neocortex is separate by the region a particular subset of the cells in the neocortex fall into. Accordingly, a widely used division refers to respective areas of the neocortex as frontal, parietal, temporal, and occipital cortices.
The frontal area comprises the motor and sensory areas, as well the analo-gous areas to the primate premotor, supplementary motor and the frontal eye
Analogy the similarity in function of two traits in phylogenetically unrelated (not sharing a common ancestor) organisms as opposed to homology which emphasizes this in phylogenetically related organisms
field (FEF). The frontal regions are distinguished by their lack of a conspicu-ous layer IV and the presense of an inner pyramidal layer from the contiguconspicu-ous parietal cortex. However, within the frontal lobe inhomogeneities such as the nonuniform thickness of layer III as well as differential characteristic molecular mechanisms utilized for communication are present.
Posterior to the frontal lobe lies the anterior part of the parietal cortex. The parietal cortex can be subdivided into three regions, the anterior, ventral and posterior parietal cortex by the cytoarchitectonical observations, though vast
Cytoarchitectonics the study of the structure
of cells discrepancies exist among authors. The somatosensory cortex of the rat fallsinto the anterior section of this region of the cortex. The posterior parietal cortex
receives extensive afferents from different areas of the thalamus.
The temporal cortex situates a number of functional networks, among them the auditory cortex. Dissimilarities in the thickness of the layers, as well as cytoarchitectonics is seen between the temporal and parietal areas.
Finally, the occipital cortex which is specialized in visual sensory functions and lies in the back of the brain, is characterized by a rather modular organiza-tion representative of differential visual space computaorganiza-tion stages.
Linking of the neocortical and the subcortical regions is facilitated through a number of intermediate processing units. The orbitofrontal, insular, cingulate, perirhinal, and retrosplenial cortices are the areas responsible for this. Specific to the interests of this report, the medial orbital, perirhinal, and the entorhi-nal cortices are intimately related to the hippocampal formation. In particular,
the perirhinal cortex, which is implicated in memory tasks (Wiig et al., 1996)
receives projections from the hippocampal formation and innervates it ipsilater-ally. Also, the retrosplenial cortex (RSC), covering the mediocaudal surface of
Ipsilateral within the same
hemisphere the neocortex is dominated by reciprocal connections with the hippocampal for-mation. It further provides indirect links between the directly linked
hippocam-pal formation and the thalamic nuclei (Vann et al.,2009). On the other hand, the
EC– which has a distinct structure, covers the hippocampus at the intersection
of the posterior and the temporal lobes, acting as the gate between hippocampus and the neocortex—projections to and from the cortical areas pass through EC. It facilitates innervations to the presubiculum (PrS) of the hippocampal region originating from the RSC.
1.2 role of the hippocampus 7
1.2 role of the hippocampus
Hippocampus has been known to play a substantive role in many aspects of
cognition, from working (Jones and Wilson,2005b;Buzsáki,2005) and episodic
memory (Buzsáki,2005), to memory consolidation (Squire,1992;Isomura et al.,
2006; Battaglia et al., 2011; Colgin, 2011) and learning (Peyrache et al., 2009;
Benchenane et al., 2010). Within the realm of spatial navigation, a multitude
of processing levels take place in the hippocampus and regions around it in-cluding the entorhinal, perirhinal and parahippocampal cortices. The role of the hippocampus in memory related abilities is also intertwined with commu-nications with the neocortical regions. Below we review the two major areas of hippocampal involvement separately.
1.2.1 Spatial navigation
Pioneering work of John O’Keefe in the 1970’s on the hippocampus of the rat provided strong evidence for the involvement of this structure as the core of
a cognitive map (O’Keefe, 1976; O’Keefe and Nadel, 1978; McNaughton et al.,
2006). In the ensuing years, a number of landmark papers were published on
the discovery of neurons specialized in the representation of space within and in the vicinity of this structure. In 1976, O’Keefe reported the discovery of the so-called “place cells” which exhibit maximal firing whenever the rats traverses a specific region in the environment it is exploring (the “place field” of the
respective place cell;O’Keefe, 1976) by integrating spatial cues and locomotive
signals (McNaughton et al.,2006).
In the 1990’s, several important works focusing on the hippocampus and
spa-tial navigation in the rat were published. Wilson and McNaughton were the
pioneers who recorded many neurons simultaneously in the freely moving rat
to gain further understanding of the neurodynamics of the hippocampus (
Wil-son and McNaughton,1993).O’Keefe and Recce(1993) reported a phenomenon
known as “phase precession”, whereby the phase with respect to the electroen-cephalographic traces recorded from the hippocampus at which place cells dis-charge advances as a function of the position of the animal within the place field
of the cell, eventually covering the whole place field in a cycle of the theta band Theta rhythm
when measured extracellularly with an electrode, the electric potential of the electrode changes rhythmically over time, encompassing a wide range of frequencies, of which frequncies between 4and 10 Hz are called theta.
frequency with precise temporal characteristics (Wilson and McNaughton,1994;
Skaggs and McNaughton, 1996; Foster and Wilson, 2007). The representaional
apparatus of space in the brain is unlikely to be limited to a set of neurons sen-sitive to visual sensory input and perhaps some locomoitve signals. In this line, “grid cells” which become active within place fields that constitute a hexago-nal lattice-like geometry with certain properties, were discovered in the 2000’s
(Hafting et al.,2005). Similar properties to those for place cells hold for grid cells
too (Hafting et al.,2008). There also exist other neurons that show idiosyncratic
activity patterns and are labeled accordingly, such as “head-direction” (Taube
et al.,1990) or “conjunctive” grid× head-direction cells (Sargolini et al.,2006).
Place cells, first reported in the 1970’s, reside in the CA1 region of the hip-pocampus and show less spatial selectivity further down the dorsoventral axis
8
introduction
of the hippocampus. CA3 also accomodates place cells which possess more specific place fields, are more reliable, and convey more information per spike
compared to the CA1 place cells (Mizuseki et al., 2012). Grid cells occupy the
dorsal Medial Entorhinal Cortex (dMEC) upstream the place cells (Hafting et al.,
2005) residing inside the hippocampal formation. Within all these directions, the
hippocampus plays a central role for the represenation and utilization of spatial
information and computations necessary to navigate the rat (McNaughton et al.,
2006;Buzsáki,2006;Burgess and O’Keefe,2011).
In addition to activity level in the two regions, when a rat is placed in a two similar but separate environments, distinct space codes are formed in CA1 and CA3, with those of the CA3 developing more slowly, suggesting more
involve-Orthogonalization separation of encoding patterns through developing statistically independent activity patterns
ment in the code orthogonalization process in an independent fashion (Leutgeb
et al.,2004). This hints at how the information processing stream may exploit
in-ternally encoded memories to produce more relevant behavioral outputs rather than simply transforming the sensory and self motion cues into output.
1.2.2 Memory consolidation and retrieval
During the course of acquisition, memories are vulnerable and are stored in a labile state. However, to retain memories, neural circuits need to transfer the information among them on various time-scales, in order to transform the un-stable memories into reliable pieces of stored information, a process known as memory consolidation. The significance of the hippocampus and its adjacent
cortical areas in preserving memories has been known after the study of
Scov-ille and Milner in 1953 and has since been extensively studied. In the reported
case (Scoville and Milner,1957), the medial temporal lobe (MTL) of the epileptic
Declarative memory Non-habitual memories, i.e. semantic and episodic memories.
patient H.M. was surgically removed due to severe conditions. The ability to re-member incidents that happened further than a few minutes earlier faded away in the patient, while he was still able to remember the memories more distant in time. Interestingly, the more remote a memory was, the more the odds that the patient would remember it. It was subsequently established that lesions to the hippocampus lead to the inability to form new declarative memories (an-terograde amnesia). The experiments on H.M. did not end soon. In fact, he was constantly studied throughout his life. H.M. has been the first, and perhaps the most important, experimental subject in memory research.
Research on memory gained further pace in the second half of the 20thcentury.
Mutual interactions among structures such as the prefrontal cortex, hippocam-pus and the nearby subcortical regions as well as intrastructure
communica-tions were shown to mediate the process of consolidation (Louie and Wilson,
2001; Lee and Wilson, 2002; Laroche et al., 2000; Squire et al., 2004; Nguyen,
2008). Theories have also been proposed on the details of the establishment of
memories (Marr,1971;Buzsáki,1989).
The life span of memories can be very extensive. As the brain is exposed the new sensory input from novel experiences, episodes of memories of the pertaining cues interpreted in the neocortex are projected to and encoded in the hippocampus. For immediate use, this can prove effective, yet if the
mem-1.3 lfp oscillations, phase-locking and temporal referencing 9
ory is necessary to be accessed in the future, it should first be stored within a reliable resource as the hippocampus is but a temporary holder of mnemonic information. Through synaptic modifications, the plastic links within neocorti-cal neural populations are altered via the redirection of the information that
is currently being held in the hippocampus (McClelland et al., 1995). At
var-ious modes of activity, including different stages of sleep (Louie and Wilson,
2001; Lee and Wilson,2002) and resting (Davidson et al., 2009; Peyrache et al.,
2009), activity traces that have already been observed during prior experience
are spontaneously reactivated in the hippocampus (Wilson and McNaughton,
1994;Skaggs and McNaughton,1996) and communicated back to the
appropri-ate areas in the neocortex (Laroche et al.,2000;Wiltgen et al.,2004), theoretically
supporting the long-term retention of them (Buzsáki,1989).
The reverse effect, namely the reactivation of neocortical traces and the
in-fluences they exert on hippocampal neuronal ensembles (Hoffman et al., 2007)
constitutes the next stage in the process of consolidation (Sutherland and
Mc-Naughton, 2000). Throughout this stage, sharp waves – high-amplitude
deflec-tions in the electroencephalographic (EEG) traces recorded from the hippocam- EEG trace
in the rat, the electroencephalographic fluctuations sampled with electrodes inserted into the brain, also known as LFP trace
pus – coincide with fast, transient ripple oscillations (lasting 30–100 ms with a frequency of 100–200 Hz), and are thought to be important in communication
in the brain for the consolidation of memory (Buzsáki, 1986; Sirota et al.,2003;
Battaglia et al., 2004; Diba and Buzsáki, 2007). After memories of events have
stabilized in the neocortex they may yet again be transmitted to the hippocam-pus, possibly through separate channels than those used for acquiring them
(Rivest,2011), in order for them to be utilized in behavior and decision-making
(Peyrache et al.,2009).
1.3 lfp oscillations, phase-locking and temporal referencing Maybe the most notable physiological feature of the brain of animals is elec-trical potentials generated by gradients in the concentrations of the ions that abound in brain cell populations. By implanting an electrode into the extra-cellular space in the brain, depending on the behavioral state of the animal, constantly changing electrical potentials can be measured. The ubiquity of these electrical fields is an intrinsic property, which when expressed in a spatiotempo-rally coherent manner within a group of neurons in the vicinity of one another can be constructively superpositioned to bring about larger-amplitude traces
labeled Local Field Pontential (LFP), rendering oscillatory rhythms prevalent in
the brain. Therefore, these electrical currents reflect underlying dynamics of neuronal actvity in concert. Precise timing in the LFPs and the structures under their influence is a crucial issue, and its absence may jeopardize the survival of
the living organism (Buzsáki,2006;Buzsáki et al.,2012).
Notably, the brain is a highly dynamic system which consists of a number of components organized in a hierarchical manner—modular structures are re-sponsible for distinct functions in a macroscopic perspective, with each module comprising submodules. In this hierarchy, the components need to communi-cate at various functional levels in order to effectively carry out vital
compu-10
introduction
tations necessary for the organism to survive. Among the distinct cognitive functions, memory systems rely extensively on the hippocampus and the pre-frontal cortex. Mnemonic traces need to be transmitted back and forth across the two structures for the storage and the retention of information. Besides, the hippocampus is involved in spatial navigation, too. Spatial information should to be delivered from the sensory systems to the hippocampus and from the hippocampus to other areas such as the prefrontal cortex so that appropriate decisions regarding locomotion be made. A possible channel through which these elements may route the flow of information and communicate is the
oscil-latory activity patterns observed throughout the brain (Salinas and Sejnowski,
2001;Canolty and Knight,2010;Akam and Kullmann, 2010;Buzsáki and Diba,
2010).
Oscillations provide a feasible infrastructure for communication by offering an orchestrating temporal reference to neuronal populations through adjusting the afferents to those cells. The most obvious mechanism to exploit a periodic signal to synchronize the activation in two or more networks of neurons is the utilitzation of the instantaneous phase of the signal. In this line, phase locking is the phenomenon whereby the probability of cell discharge increases at certain phases of a reference EEG trace, consequently causing the spike distribution to become biased towards a preferred phase. Phase locking occurs in different frequency bands and brain regions. Within the hippocampus a large propor-tion of CA1 neurons, as well as neurons in the neighboring regions fire at a
preferred phase of hippocampal LFP fluctuations.Siapas et al.(2005) were the
first to demonstrate that a significant portion of the prefrontal neuronal popula-tions become phase locked to the hippocampal theta oscillapopula-tions in the rat brain while the animals were engaged in a behavioral maze task (see below). Similar
reports have shown this effect elsewhere in the brain (Sirota et al.,2008). Their
results suggested the role of locking in interareal communication via evidence for directionality of locking effect. During slow wave sleep (SWS) prominent,
Slow-Wave Sleep a stage of non-REM sleep with characteristic slow (≤1 Hz) EEG oscillations along with large-scale synchronized activity in the neocortex
yet short-lived high frequency ripple oscillations originating from the HC dom-inate the brain. Spontaneous spiking activity in the prefrontal areas becomes tuned to these ripples, theoretically supporting the consolidation of memories
(Battaglia et al.,2004).
Fast oscillations such as gamma (30–80 Hz) are involved in mediating atten-tion in the visual cortex. With increased attenatten-tion, informaatten-tion is transferred
from V4 to the frontal eye field (FEF) for further processing (Gregoriou et al.,
2009). Furthermore, selective responses to visual stimuli properties such as
ori-entation have been shown to correlate with the phase of gamma frequency and the corresponding synchronization facilitating maximal selectivity with
mini-mal noise in the firing rate characteristics (Womelsdorf et al.,2012).
On the slower end of the spectrum of frequencies observed throughout the brain, theta rhythm (4 – 12 Hz) is the quintessential characteristic of hippocam-pal LFPs. It is the dominant frequency band in the hippocampus most promi-nent during active exploration, REM sleep and consummatory behavior, and is
Rapid Eye Movment a stage of sleep characterized by rapid movement of eyes also accompanied by several other factors such as low-amplitude EEG traces
implicated in various functions such as spatial navigation in rodents (Winson,
1.4 communication within and beyond hc-pfc circuitry 11
2008; Brandon et al., 2011) and humans (O’Keefe et al., 1999; Ekstrom et al.,
2005;Watrous et al.,2011), speech and language processing (Giraud and
Poep-pel, 2012; Kraus,2012), memory encoding, retrieval (Skaggs et al., 1996; Mehta
et al., 2002; Siapas et al., 2005) and consolidation (Squire, 1992; Buzsáki, 2005;
Buzsáki, 2006; Benchenane et al., 2011), information integration (Womelsdorf
et al.,2010;Battaglia et al.,2011) and can be impaired as a consequence of
neu-rological disorders (Sigurdsson et al., 2010). During active behavior, a majority
of the cells in the CA1 region, as well as a smaller number of cells in the CA3
(Mizuseki et al., 2012) of the hippocampus become phase locked to the theta
rhythm. It is believed that information exchange in the brain, and in particu-lar between the hippocampus and surrounding areas and the frontal areas in
the cortex is facilitated by phase locking to the theta rhythm (Battaglia et al.,
2011). Further, oscillations in the theta band afford the representation of space
and their disruption diminishes the ability to accurately encode information
(Winson,1978;Koenig et al.,2011).
Among the theories proposed concerning information transfer, the two-stage theory posits that information is transferred in a rather unconventional manner— the transmission is bidirectional (reciprocal) and both parties are actively
en-gaged in the process (Buzsáki and Diba,2010). In this manner, a target structure
starts the conversation by inducing a phase-locked spiking activity in the sender structure (source) by which the information is sent during a period when the destination is most ready to receive information (“perturbation cycle”). In the
awake animal, theta-modulated gamma activity in the cortex (Sirota et al.,2008)
is temporally biased by the hippocampus such that information is transferred to the hippocampus so as to exert maximal effects on the hippocampal networks. In SWS, however, sharp waves in the neocortex stimulate hippocampal activity
in order for the information to be transferred to the neocortex (Battaglia et al.,
2004). In addition, alternative models emphasizing the continued involvement
of the hippocampus in retrieving spatial and episodic information have also
been proposed (Nadel et al.,2000).
Although static locking of firing to a reference EEG trace may be crucial to information processing, it is not the whole story. As discussed earlier, having started at a particular theta phase during spatial navigation, place cells fire at progressively earlier phases in successive theta cycles. The phase precession ef-fect is consistent throughout the place field in the sense that each spot within the place field marks the phase at which the corresponding neuron will fire. Phase precession is not limited to hippocampal populations and has been
doc-umented in the medial prefrontal cortex (mPFC) of the rat as well (Jones and
Wilson,2005a), suggesting a more global functional role of the effect with
possi-ble implications for temporal code. Taking the hippocampal LFPs as reference, this could have important functional implications for the accuracy of spatial representation and synaptic modification in the brain.
1.4 communication within and beyond hc-pfc circuitry
Communication is the key for the neural populations to develop networks of in-terdependent computation. To this end, mechanisms should be utilized to route
12
introduction
the output of local networks to the appropriate neural ensembles for further processing and also to integrate such information delivered by the orchestra-tion of coactivaorchestra-tions in segregated neuronal ensembles at a more global level. As suggested by many researchers enumerated earlier, the rhythmic activity of brain cells could provide an infrastructure of communication, with low- and high-frequency couplings implicated in high- and low-range transmissions,
re-spectively (Siegel et al.,2012;Buzsáki and Chrobak,1995).
In the domains where the hippocampus is a major participating actor such as memory construction, the employment of behaviorial tasks has helped re-searchers to identify information exchange between the frontal areas of the neocortex and the hippocampus. This exchange of information takes place at different stages, including sleep and during active behavior. Many reports have documented evidence for the role of hippocampo-cortical interactions during sleep. In SWS, coupling is observed between the HC and the somatosensory
during SWS sleep (Sirota et al., 2003), REM sleep and active behavior (Sirota
et al.,2008).Siapas et al.(2005) have demonstrated a short time-lag between the
oscillations originating in the hippocampus and the corresponding prefrontal phase-lockings, consistent with the idea of directionality of the entrainment of prefrontal neurons during active behavior.
However, information exchange is not limited to HC-PFC pathways. When an animal is exploring an environment, sensory input must be integrated at different levels for the animal to act optimally and survive. The hippocampus is heavily involved in spatial navigation with spatial information processing
taking place at different stages in its circuitry (Leutgeb et al., 2004; Isomura
et al.,2006;Hafting et al., 2008;McNaughton et al.,2006;Kjelstrup et al.,2008;
Mizuseki et al.,2012). Moreover, information about the representation of spatial
cues and navigational maps, along with the sensory input from other regions should be encoded and further processed in the brain, either directly or after
having been processed at intermediate stages (DeCoteau et al., 2007;
Seiden-becher et al.,2003). The integration of such information demands complex
com-munication channels encompassing all neuronal circuits in the brain, raising the possibility of the existence of links between diverse structures and the HC, as well as the role of the HC as a coordinator of communication via providing a
ref-erential clock (Salinas and Sejnowski,2001;Akam and Kullmann,2010;Buzsáki
and Diba,2010).
Furthermore,Sirota et al.(2008) show that highly localized gamma bursts in
the neocortex are entrained by the theta oscillations arising from the hippocam-pus, with the faster gamma band being more strongly modulated. The evidence showing the link between the gamma oscillations and local engagement of
neu-ral networks (e.g. Gray and Singer, 1989), along with these results support a
synchronizing effect and a coordinating role for the hippocampal theta, linking remote structures in the neocortex by providing a temporal framework for their
communication. In line with the above observations,Womelsdorf et al.(2010)
re-port that the spectral power of the theta signal in the rat rises at decision points in a maze, supporting the hypothesis that this rhythm plays out a role in linking remote structures and facilitating information integration to guide behavior.
2
R E S U LT S
The main goal of this project was to build map-like representations of the modu-lation of activity across neocortex. Using the Rayleigh test and also the Pairwise
Phase Consistency (PPC) (see Appendix A) we investigated if the firing
activ-ity of the recorded neurons was modulated with respect to the phase of the
hippocampalLFP. A unimodal phase modulation was confirmed in a subset of
cells, while in other cells a bimodal phase distribution was found. Moreover, we observed that the level of phase-locking varied with time. We further tested
the coherency level (as defined in Section B.3) of the neuronal firing acitivty
and, while confirming the time-varying nature of the level of modulation/co-herency, found that on average not only are the cells modulated within the theta frequency band, but also they are coherently active with respect to the second harmonic frequency band of theta (16 – 18 Hz). These results are presented in further detail in the upcoming sections.
2.1 theta modulation across neocortical sites
We first started by extracting the phase of the spike trains from the collected data and using Rayleigh cicular test statistic to obtain p-values for the null hypoth-esis of uniformity against any alternative. For each individual session a map of distribution was constructed with statistically significant sites differentially pronounced in the figures. The full list of maps obtained in form of the
distri-bution histograms of the spike phases may be found in Appendix C. Figure 2
summarizes the map of the proportion of modulated cells in neocortex.
The fraction of the recorded cells entrained with respect to the theta rhythm varied as a function of the location of the recording tetrode. In line with previous
reports (Siapas et al., 2005;Sirota et al., 2008) we found a larger proportion of
modulated cells in the frontal and parietal areas. Moreover, a number of sites at other locations also had a significant number of modulated cells. For instance,
20% of the neurons at the temporal recording array one site (H12; Figure 2)
were modulated significantly (p < 0.05, Rayleigh test). With all the recorded
neurons considered, the fraction of significantly modulated cells is 0.061 and
0.049 at α =0.05 and α= 0.01 respectively. These figures together indicate that
there exist certain areas throughout the neocortex that have neurons entrained
14
results
8% < 1% 10% < 1% < 1% 10% < 1% < 1% 11% < 1% < 1% 17% 25% 5% < 1% < 1% < 1% < 1% < 1% < 1% 8% 11% < 1% 7% < 1% < 1% < 1% < 1% < 1% 20% < 1% 6% < 1% 4% < 1% < 1% 5% < 1% 5% < 1% < 1% < 1% < 1% 7% 14% < 1% < 1% < 1% < 1% 25% 8% < 1% < 1% < 1% 8% < 1% < 1% < 1% < 1% < 1% < 1% 7% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 13% < 1% 13% 13% < 1% < 1% < 1% 5% 13% 5% 10% < 1% < 1% < 1% < 1% 6% 8% < 1% < 1% 8% < 1% < 1% < 1% < 1% 9% < 1% < 1% 4% < 1% < 1% < 1% < 1% < 1% < 1% 14% 6% 4% < 1% 8% < 1% < 1% 13% < 1% < 1% < 1% < 1% < 1% (a) < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 17% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 7% < 1% < 1% < 1% < 1% < 1% 20% < 1% < 1% < 1% < 1% < 1% < 1% 5% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 14% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 7% 7% < 1% < 1% < 1% 5% < 1% < 1% 10% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 14% < 1% < 1% < 1% 8% < 1% < 1% 13% < 1% < 1% < 1% < 1% < 1% (b)Fig. 2: The relative modulation map of the neurons recorded at each site. Each pie chart piece displays the fraction of the cells that were modulated with respect to the hippocampal theta rhythm acquired in the CA1 field (recording tetrode row A is at the bottom and row L is on top). Neurons with a firing rate of less that about 0.9 were excluded. The Rayleigh test was used with the α value set at 0.05 (a) or 0.01 (b). It can be seen that there exist sites whose neurons are entrained at a proportion close to the Type I error (a) which implies that the detected effect cannot be trusted. However, panel (b)
demonstrates a subset of those neurons are highly modulated and that the proportion that this subset represents is sufficiently higher than the Type I error. Therefore there exist some sites are strongly entrained while others are detected to be entrained at the chance level, and yet others are not identified as modulated.
with respect to the hippocampal theta, while in other areas no (or a very small number of) neurons are modulated. This result extends previous findings in that new prospects are confirmed as for theta rhythmicity to have a more global involvement in distinct functional roles.
2.1.1 Time dependent theta modulation
Although overally some sites were significantly modulated by the theta phase of
theLFPrhythm from the hippocampus, the effect was not detected persistently
throughout a session of acquisition. In fact, within confined periods the spikes emitted from neurons were highly modulated and within other periods no or little modulation was there. This was confirmed both by means of statistical
tests and spectral analysis (see Section 2.2). First, a dilating moving window
was used to calculate the p-value of the phase distribution comprised within
the window (Figure 3). Iteratively, at any given step, a subset of all the spikes
falling into a temporal window with a certain width was considered. Once the width of the window was set, it was moved from the beginning to the end of the recording session in steps equal to half the width of it. In the end the width of the window was increased and the sliding procedure was repeated. This was iterated until the window covered the whole session.
2.1 theta modulation across neocortical sites 15
Window offset ((Y+1)*10)
Window width (/20−1)
Session 11, site D12 A moving window of variable length (the upper on the Y axis, the larger the width)
with variable steps (equal to the half of the width of the window, X axis). The second column shows modulation around 30 (on Y axis) which suggests that the spikes near the middle of the spike set are more modulated, supporting the observation
of the blue area in the first column near Y=50. The black superimposed curves are visual approximations to the windows with
non−empty intersection. The lower the curve, the more to the left the intersection.
10 20 30 40 50 60 10 20 30 40 50 60 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 (a) Session 11, site L8 A moving window of variable length (the upper on the Y axis, the larger the width)
with variable steps (equal to the half of the width of the window, X axis). The rather homogeneous blue color on the left−most column suggests a short period
of good modulation, with no or little modulation afterwards. The light blue in (1,2) suggests this period has occured within the first 60 seconds.
10 20 30 40 50 60 5 10 15 20 25 30 35 40 45 50 55 −3 −2.5 −2 −1.5 −1 −0.5 (b) (c)
Fig. 3: Modulation level varies with time. Shown are the sliding window modulation maps for two example cells in session 11, sites D12 and L8. (a) The second column shows modulation around 30 (on Y axis) which suggests that the spikes near the middle of the spike set are more modulated, supporting the observation of the blue area in the first column near Y=50. The black superimposed curves are visual approximations to the windows with non-empty intersection. The lower the curve, the more to the left the intersection. (b) A moving window of variable length (the upper on the Y axis, the larger the width) with variable steps (equal to the half of the width of the window, X axis). The rather homogeneous blue color on the left-most column suggests a short period of good modulation, with no or little modulation afterwards. The light blue in(1, 2)shows that this period has occured within the first 60 seconds. (c) The preferred phase of the spikes in the activity of cell 11D12 are depicted in the form of a 3D histogram. This figure is another perspective on the first column ofFigure 3a. The vertical axis (Z) is the count in each bin, and the horizontal axis (X) is the spike phase in radians. The oblique axis (Y) shows the width of the window starting from the beginning of the session (and extending up to the corresponding point of the Y axis). An evident dynamic variation in the distribution of spike phases can be seen in that the rate of increase in the Y direction is not monotonically increasing. The p-value corresponding to each level (each individual histogram extended from left to right along the X axis) can be found on the respective Y value of
Figure 3a. The rainbow coloring is merely for visualization purposes and has no particular meaning.
The above observation was also confirmed by means of constructing the
co-herogram of neuronal acitivty via spectral analysis (Figure 7). The coherograms
revealed cross-frequency the coherency of the spike trains throughout the
ses-sions. As can be seen in the sample in Figure 7a, the level of coherence varied
with time, consistent with the result of statistical tests presented above. Further
16
results
< 1% 7% 18% 5% < 1% < 1% 14% < 1% < 1% 6% < 1% < 1% < 1% 5% < 1% < 1% < 1% < 1% < 1% < 1% 14% < 1% 7% < 1% < 1% < 1% < 1% < 1% < 1% 20% 10% < 1% 13% 4% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 17% 13% 13% < 1% < 1% 14% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 6% < 1% < 1% < 1% < 1% < 1% < 1% 7% 8% < 1% 18% 8% < 1% 11% < 1% < 1% < 1% 8% 22% 7% < 1% < 1% < 1% < 1% 13% 5% 10% < 1% 25% 17% 33% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 9% < 1% 7% < 1% < 1% 10% < 1% < 1% < 1% < 1% 14% 6% 4% < 1% 8% 33% < 1% < 1% 8% < 1% 25% 13% < 1% (a) < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 7% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 7% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 4% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 7% < 1% < 1% < 1% < 1% < 1% 5% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 9% < 1% 4% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% 4% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% (b)Fig. 4: The relative modulation map of the neurons recorded at each site. Shown are the relative count of the number of bimodally modulated cells to total recorded cells per recording site. The maps in panels (a) and (b) are constructed with α=0.05 and α=0.01 respectively. Simimilar to maps in
Figure 2, it can be seen that a relatively large proportion of all cells have two preferred firing phases with p<0.05 under the Rayleigh test, whereas a very small proportion shows bimodal modulation
with p<0.01. Note the dispersion of the entrained neurons is biased towards the frontal areas.
2.1.2 Bimodal modulation
The Rayleigh test is a statistical test of the null hypothesis of uniformity against any alternative. Therefore, if a test turns out to be significant, this information cannot be used crudely to assess what the actual distribution might look like. In order to reveal any bimodal modulation effect in the data set, we multiplied the extracted theta phases by a factor of two and tested the resulting set for
Fig. 5: Sample maps of bimodally modulated neurons. (a) and (b) show the distribution of the angles of two sample sessions with highly significant (p<0.05, Rayleigh test) neurons’ distribution
represented in darker shade. The respective angles were first multiplied by 2 and tested for uniformity (see text).
191 228 709 802 29 56 1578 1684 109 170 1618 1804 242 317 1275 1350 77 116 273 303 190 257 57 82 252 309 219 265 74 124 323 403 229 297 374 444 121 190 599 668 216 245 351 408 130 165 459 559 332 396 9 31 114 170 84 131 150 182 217 279 22 37 1011 1106 37 54 58 86 44 66 283 317 1437 1558 14 33 88 124 28 48 179 236 796 852 64 103 173 250 349 400 148 187 618 688 471 525 109 149 82 114 121 151 48 76 477 557 621 735 260 293 179 206 74 119 362 412 580 656 513 577 757 828 99 144 75 105 16 35 8 29 561 626 88 136 1189 1278 141 183 421 506 41 79 131 171 56 85 188 230 (a) 42 77 72 116 398 451 55 89 2503 2587 8 35 311 365 353 396 853 946 12 26 265 312 185 224 264 311 389 453 182 225 1819 1887 44 66 73 109 70 114 347 407 529 587 148 204 333 363 126 165 64 97 103 137 19 51 72 97 80 118 382 433 210 230 27 55 145 184 1854 1956 87 126 40 79 69 115 1453 1590 1265 1375 111 155 119 160 264 321 77 104 283 335 16 38 20 47 288 330 246 285 51 76 239 290 253 311 181 227 681 734 346 385 328 377 59 100 12 37 64 89 131 177 72 113 273 311 127 164 204 229 42 72 28 59 (b)
2.1 theta modulation across neocortical sites 17
uniformity using the Rayleigh test statistic (Peyrache et al.,2011). As a result, it
was discovered that a smaller proportion of the neurons had a bimodal distribu-tion of preferred firing phase than those with a unimodal distribudistribu-tion discussed
earlier. Figure 5 demonstrates the fraction of the cells modulated in each
neo-cortical acquisition site.
Consistent with the expectation from previous results on unimodal theta entrainment, the majority of the cells that showed bimodal modulation lied near the frontal and parietal areas near the midline. Overally, 5.2% of the total recorded cells (excluding the neurons with a firing rate of below the
predeter-mined threshold of 0.9 Hz) showed modulation at α =0.05 and 0.7% at α=0.01.
However, locally the percentage of the modulated cells would rise to as high as 33% in the anterior cingulate area. Interestingly, cells from the somatosensory cortex did not show significant levels of modulated activity. The results confirm the existence of neurons spread out over the neocortex which possess two pre-ferred phases of firing with respect to theta. Furthermore, the observed effects are not as strong as results on unimodal modulation discussed earlier.
2.1.3 Using the PPC measure to confirm modulation
The Rayleigh test is biased in the size of the population in that the larger the populations gets, the smaller the p-values obtained will be, regardless of the actual distribution of the data points. To control for this potential shortcoming,
thePPC was used on the same data set. Unlike the Rayleigh test, thePPCtakes
pairs of data points and bases the statistical measure on those so that the
num-Fig. 6: PPC vs. Rayleigh p-value comparison. (a) For a sample neuron, a cross-frequency “coherence” plot is shown using either the Rayleigh test statistic (top) or the PPC measure (bottom). The−norminv normalization was used (inverse of the normal probability distribution function) to normalize the p-values. For both graphs the X axis is frequency (Hz) and the Y axis is the (transformed) respective value. The same set of spikes were used. Using bins of width 1 Hz at steps of 0.5 Hz the respective phase of the spikes were extracted and the resulting set was used to obtain a p-value or the PPC value. (b) The scatter plot of PPC values versus the log of p-values for a different cell than in (a). (c) Similar to (a) but for a different cell and also a different normalization for p-values (-log; in red). Correlation coefficient is 0.8813. 2 4 6 8 10 12 14 16 18 20 −2 0 2 4 1C11 −norminv(p rayleigh) 2 4 6 8 10 12 14 16 18 20 −0.02 0 0.02 0.04 0.06 PPC correlation = 0.9580 (a) (b) (c)
18
results
(a) (b) (c) 0 5 10 15 20 25 30 35 40 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 (d)Fig. 7: Coherogram of a sample cell reveals highly modulated bouts of activity. (a) The coherogram of cell 8G1 is shown. For short periods of time (extending up to about 20 seconds) spike train becomes highly coherent with respect to a narrow frequency band (with a coherency value of up to 0.9). (b) Extending mean of the coherogram presented in (a). A dilating window comprises the portion of the coherogram starting at t=0 through t=t0where t0is increased stepwise (slides through the end).
In the beginning where the variance is expected to be high (because a small subset of the information is being used) variability at different frequencies is relatively high. Progressing through the end, however, the average coherency stabilizes. The final portion of this graph shows the average
coherency of the spiking activity of one cell in a whole session. Note that two spots at the theta band and its second-harmonic displays a pronounced level of coherence. (c) The magnified version of the red portion at the end of the time axis in (b). (d) The 2-dimensional graph of portion shown in (c). X and Y axes in (a-b) are time (s) and frequency (Hz), and in (d) frequency (Hz) and power, respectively. X axis in (c) is time (s) and values are color-coded. Range of variations in X axis in (c-d) is 2 – 40 Hz.
ber of points present is fully ignored, while a measure of concentration of points
is obtained (Vinck et al.,2010; see alsoAppendix A). For the same data sets the
Rayleigh test and the PPCperform similarly (Figure 6). Although there may be
clear differences, the resulting maps resembled those obtained via the use of the Rayleigh test. Like before the maps constructed using the latter method were made using only the cells with a mean firing rate of about 0.9 Hz (emitted at least 1000 spikes in a session of about 17 to 20 minutes).
2.2 coherency detection using spectral analysis
Using Chronux (Bokil et al., 2010) we investigated whether coherency effects
2.3 spectral analysis reveals uniform second-harmonic locking of neocortical neurons 19
The coherogram of a number of cells was made and it was observed that the coherency is not consistently present throughout the session or within the exact same frequency band. Highly coherent bouts of activity were seen along with
wider, less coherent periods in all cells (Figure 7a). By calculating the average
level of coherency an interesting effect was observed. The coherency level was invariably higher not only in the theta band – which was the main point of interest here – but also in a relatively wider frequency band at about the and
where one would expect the second-harmonic of theta to be (Figure 7b).
Fol-lowing the examination of a few random neurons to check whether this effect is present in more cells (which was confirmed), a naïve approach (simply av-eraging the coherogram from all the recorded neurons) was taken in order to test the whole data set at the broadest sense possible. Had we detected no ef-fect via this approach, we would have inspected the data further using more sophisticated methods. However, were any effect identified in this fashion, we would have been a step closer to the goal with less effort. Ultimately, a surpris-ing phenomenon was observed which we discuss in further detail in the next section.
2.3 spectral analysis reveals uniform second-harmonic lock-ing of neocortical neurons
Following the detection of second-harmonic locking by averaging the cohero-grams of a subset of cells, the averaging was repeated for all the recorded cells.
Once again, this effect was strikingly clear as manifested in Figure 10e. In
or-der to control for potential side effects of the parameters used to obtain the all-cell coherograms, the same procedure was iterated on different subsets of cells and with tweaked parameters. This, however, did not change the final ef-fect observed radically as the higher coherency at the band extending between
15 Hz and 19 Hz was observed invariably (Figure 10a-10d).
We further looked into this phenomenon by computing the autocorrelograms of the spike trains to qualify the peaks observed. Despite no similarly persis-tent phenomenon in all the cells as before, the absence of the effect could be attributed to the fact that the autocorrelation function of a spike train reveals exact interspike phase relationships, whereas the Hilbert transform used to
ex-tract the phase of spikes from the filteredLFP(see the chapter onMethods) takes
into acount temporal variations of the theta spectral power and thus depending on the behavioral epoch under consideration the appropriate phase values are used. To delineate this point with a simple example, consider a compound two-cycle signal composed of two concatenated signals each lasting one two-cycle, one with an exact frequency of 6 Hz and the other a frequency of 7 Hz. Using the Hilbert transform to extract the phases of a given spike train will yield results different from an autocorrelogram of the same spike train. This fact is also re-flected in the autocorrelograms displayed here in that no one single peak is observed and rather several peaks of comparable amplitude can be seen. This
20
results
−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0 1 2 3 4 5 6x 10 −6 time lag (s) correlationFig. 8: Autocorrelogram of a sample cell displaying phase-locking to the theta and its second-harmonic band.
Following the detection of the second-harmonic modulatory effect of the theta rhythm, we strived to disentangle potentially direct relation-ships with the theta band itself. At least two possibilities are suspected to be the case. First, the observed phe-nomenon may simply be an artifac-tual result of strong locking to the conventional theta frequency band (6 – 10 Hz). In this case, the fact that the cells are coherent with respect to the theta rhythm entails the presence of some level of locking at the signal’s second harmonic band. Therefore, a lower coherency level would be expected to be observed which as is visible
in Figure 10e is not the case. Furthermore, the width of the frequency band
in which the effect is visible is not considerably wider than the slower phase-locking. Second possibility would have been the existence of a beta-band
pace-maker of the LFPsimultaneously active at or close to the CA1 field of the
hip-pocampus, or alternatively a mechanism influencing the activity of the theta pace-maker of the hippocampus and/or the neocortical neurons arising the question whether multiple oscillatory mechanisms might be coordinating neu-ronal activity throughout the brain. At any rate, the reported coherence of the firing activity of the pyramidal neurons across distinct neocortical areas and from distinct cortical layers is a novel effect that under comparable experimen-tal settings has not been reported in the past.
Fig. 9: Hilbert transform and autocorrelation function may produce distinct resutls. The second cycle in the above example signal is double the frequency of the first cycle. Assuming as an illustrative example that the above signal has been band-pass filtered, the application of the Hilbert transform on the spikes (red bars) will yield the spike phase sequencehπ
4,π4,π2,π2iwhich is modulated to the
descending phase of the signal, while if the autocorrelogram of the spike train is plotted, two peaks will become pronounced with one located half-way the time of the occurrence of the other.
−1 −0.5 0 0.5 1
2.3 spectral analysis reveals uniform second-harmonic locking of neocortical neurons 21
(a) (b)
(c) (d)
(e)
Fig. 10: Average coherency in theta and its second harmonic across different subsets of cells with
different analysis parameters. The color-coded cross-frequency coherogram of spiking activity of
each single cell in a subset of all the cells with respect to the hippocampal CA1 LFP has been computed using multi-taper spectrum estimation. Since different parameters in the multi-taper method essentially influence the smoothing and resolution of the final figure, distinct parameters were used in multiple runs to ensure that the effect observed was not an exaggeration of a smaller artifact. The uniform second-harmonic coherency is visible invariably across subsets and despite the change of parameters. A sliding window of width 10 seconds in steps of 2.5 seconds used in (a) and (b), a window width of 6 and 10 seconds, respectively, in steps of 500 ms in (c) and (d). The taper parameters were set to [4 6] and [10 19] in (a) and (b-d) respectively. Panel (a) and (b) show the coherogram corresponding to the cells recorded in sessions 5 through 10, panels (c) and (d) show the coherogram for data collected throughout sessions 1 to 30 and 1 to 25. Panel (e) demonstrates the coherogram of all the neocortical cells recorded in 43 sessions, computed with a sliding window width of 30 seconds in steps of 1 second, and taper parameters of [10 19]. X ranges over the whole session recording time in all panels. Y axis ranges from 2 to 40 Hz in (a-b).
