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Averaging Transformations of Synaptic Potentials on Networks

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The problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is introduced that simulates the internal information processing of brain compartments. Synaptic potentials are integrated over small number of realistically coupled neurons to obtain macroscopic quantities. The striatal complex, an important part of the basal ganglia circuit in the brain for regulating motor activity, has been investigated as an example for the validation of the model.
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Averaging Transformations of Synaptic Potentials on
Networks
H. R. Noori,a
aInterdisciplinary Center for Scientific Computing, University of Heidelberg, Im
Neuenheimer Feld 294, 69120 Heidelberg, Germany
Abstract
The problem of the transformation of microscopic information to the macro-
scopic level is an intriguing challenge in computational neuroscience, but also
of general mathematical importance. Here, a phenomenological mathematical
model is introduced that simulates the internal information processing of brain
compartments. Synaptic potentials are integrated over small number of realis-
tically coupled neurons to obtain macroscopic quantities. The striatal complex,
an important part of the basal ganglia circuit in the brain for regulating motor
activity, has been investigated as an example for the validation of the model.
1. Introduction
The brain nuclei, as parts of complex brain networks, are comprised by
different types of inter- and projection neurons within subnetworks of highly
complex structure. Beside the anatomical formation, functional properties in
integration and processing of neural information become adapted during the
development of these regions until adolescence. In this study, adult brain nuclei
are considered after their final development, as part of information processing
pathways.
Experiments on the topology of brain regions suggest that these structures
can be categorized as heterogeneous media. There are various mathematical
methods describing dynamical processes in heterogeneous media, such as asymp-
totic analysis, homogenization, and integral equations (Pavliotis and Stuart [17],
Haken [13], E and Engquist [8], Levin and Chao[15]). There are traditional net-
work approaches on the effects of properties such as the local connectivity of
neurons on the striatal function (Wickens et al. [21]). These studies concen-
trate merely on the network structure of a particular brain region e.g. striatum
and even then do not contain some important features such as the role of large
spiny neurons in the striatal function. Large spiny neurons in the striatum are
Corresponding author
Email address: hamid.reza.noori@iwr.uni-heidelberg.de, hnoori@princeton.edu (H.
R. Noori)
Submitted Preprint June 18, 2009
Nature Precedings : hdl:10101/npre.2009.3348.1 : Posted 19 Jun 2009
cholinergic and are of great importance for processes involving addiction and
food intake (Rada et al. [18], [19], Avena et al. [1]).
In the present study, simplified but essential physiological processes have
been chosen as the biological foundation for the mathematical model. The
reader is advised to consider the appendix for a brief introduction into the
biological terminology.
The course of information processing in brain regions depends on the propa-
gation of synaptic potentials - which are averaged postsynaptic potentials - along
the subnetworks of these regions. Thus, understanding the physiology of this
integration process requires the comprehension of the neuronal architecture of
the brain region of interest. The regional subnetworks consist of different types
of neurons and characteristic connections among them that can be obtained
by experiments. In this study the intraneuronal connections are subdivided
into the global, and ultrastructural morphology. Golgi and immunohistochem-
ical methods provide optimal frameworks for obtaining the values of the two
morphological dimensions experimentally. The immunohistochemical studies
reveal the appearance of certain neurotransmitter systems in a structure; Golgi
studies provide information about the form and type of neurons expressing the
obtained neurotransmitter systems and on the morphological dimensions of the
brain region in terms of the characteristic connections between different types
of neurons in a brain region. In general, the structural topology of the brain
region is then obtained. The knowledge about the appearance of different types
of neurons and the intraneuronal synaptic interactions inside a nucleus allow us
to abstract its structure through networks.
One way of representing such networks is through their realization in con-
tinuous spaces. The attendance of a high amount of neurons supports the idea
of the appropriateness of such an approach for this purpose.
Because of the importance of the global and ultrastructural morphology for
the information integration process in a nucleus and the dependency of their
values on the spatial distribution of neurons, they shall be modelled as spatial
variables parametrized by the neuron (neurotransmitter) type.
To provide a general framework for the regional neuronal activity, we intro-
duce an integral operator averaging the information on two refinement scales.
The idea is to cover the space including the nucleus with copies of discrete
fundamental domains consisting of neuronal assemblies which we call n-cells.
Roughly spoken, n-cell patches are finite networks of neurons. The ultrastruc-
tural morphology of a nucleus in terms of the synaptic connectivities between
different neurons provides information on the local connectivities in the n-cells,
which are embedded as edges of neuronal network inside the n-cells. Within the
information on the adherence functions of n-cells (global morphology variables)
and the distribution of neurons, the averaging of synaptic potentials across the
network of nuclei is completed. The main advantage of this method is in its
appropriateness for applications on various brain regions.
Assembling a suitable number of n-cells by considering the large-scale inter-
action between the n-cells (adherence of n-cells), we obtain information on the
combined influence of several synaptic inputs on macroscopic neuronal activity
2
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Figure 1: Composition of n-cells
(Fig. 1). One trivial example is the subthalamic nucleus which consists of only
one class of interneurons. In this case the number of n-cells under consideration
is one (Parent and Parent [16]).
The aim of this study is to present a mathematical technique for averaging
microscopic information along complex network structures such as the networks
of single brain regions. The technique is applied on the corpus striatum - a part
of the basal ganglia circuit which plays an important role in the regulation of
motor behaviour- and shown to mimic faithfully the qualitative oscillatory be-
haviour of this brain region. The general formulation of the averaging operator
suggest its suitability for other discrete multiscale problems, especially in the
research area of material sciences.
2. Model Statement
Statement:. The integration of the electric activity in a brain nucleus (infor-
mation processing) depends on the distribution of its comprising neurons, the
ultrastructural morphology as a local variable quantity and the global quantity
3
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in terms of the composition of neuronal fundamental domains (n-cells), that
describes the topology of the brain region.
The concept of the n-cells is very essential for the understanding of the
averaging transformation. The idea is to path up a region with multiple copies
of discrete fundamental domains called n-cells. The n-cells compose the whole
brain region of interest by applying the global morphological properties and
contain the local morphological properties as finite graphs. Hence, they unify
the morphological dimensions into one notion.
Definition 1: A n-cell is a neuronal assembly represented by a finite graph
characterized by the local ultrastructural morphology. Within proper composi-
tion of the n-cells, as discrete fundamental domains, they patch up the region
of interest.
Let Ω R3a compact, path-connected set, be the brain region of interest.
Let ΩiΩ, iIbe a skeleton representation of the finite graph of a n-cell,
and Ibe the finite index set with #I= #{n-cells}. Furthermore, let xibe
the variable describing the network position of a neuron relative to the n-cell
i; and ythe continuity variable describing the spatial position of a neuron
embedded as points in Ω as a subset of the complete space R3.{z}denotes the
finite set of neurotransmitter families that appear in the brain region of interest.
By allocating any neuron to a neurotransmitter, zparametrizes the proposed
averaging.
Definition 2: A synaptic potential uz
x(t) is the sum of all Hodgkin-Huxley
postsynaptic potentials of a neuron of type zat position xinside a n-cell.
iI , z , xi:uz
x: [0, T ]R.
To average the synaptic potentials uz
x(t) in n-cells, the local connectivity
function ψz: ΩiR+has to be characterized. By introduction of the global
connectivity function χi: Ω R+, describing the composition of n-cells, we will
cover Ω will n-cell patches. We write χ:= (χi) for the |I|-vector of composition
mappings. The normalized distribution function ρz: Ω [0,1] as the kernel of
the averaging operator will complete the information required for the integration
of synaptic potentials across the network of brain regions. These functions
(ψz, χi, ρz) are obtained from Golgi- and immunohistochemical studies.
The continuous realization of the network structure of the brain nuclei and
the idea of transforming the microscopic, synaptic information to the macro-
scopic level compatible with the internal structure of a brain region suggest the
construction of an averaging integral operator along networks.
Definition 3: A compartment is a multiple C:= (Ω, ρz, χ, ψz, I) which
characterizes a brain nucleus by its ultrastructural and global morphology.
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Definition 4: Let Cbe a compartment, then the averaged potential v(t) of
synaptic potentials uz
x(t) across the network of a single brain nucleus is repre-
sented by:
v(t) = X
zZ
ρz(y)·PiIχi(y)(Pxiψz(x)uz
x(t))
|I|g(χ(y)) dy , [
i
i,(1)
g:R|I|R+is the proper averaging parameter estimated by immunohisto-
chemical experiments. It provides a combinatorial dimension for the composi-
tion of the n-cells in a compartment.
The universality of the concept of a compartment provides the possibility
of applying the averaging transformation of this type for a wide category of
network multiscale problems.
3. Numerical Simulations
The aim of this section is the numerical investigation of the dynamical be-
haviour of a compartment by known synaptic dynamics (in terms of electric
activity uz
x(t)) of single neurons. The corpus striatum is used as an non-trivial
example to illustrate the efficiency of the averaging operator method. The com-
plexity of the striatal structure on the one hand, and the importance of this brain
region as a substrate of the basal ganglia in the regulation of motor activity and
neurological diseases on the other hand, make it a proper representative for such
investigations. First, the main morphological and ultrastructural properties of
this compartment are summarized which are required to comprise the integral
function. These properties include the spatial distribution of the different neu-
ral populations (ρz), the neurochemical classification (z), and the intraneuronal
connections ((ψz, χi, g)). Then, the simulation results are discussed and com-
pared with the experiments.
A category of proper experiments for the validation of the numerical results
is represented by the local field potential (LFP) studies. Thereby, a signal is
recorded using a low impedance extracellular microelectrode, placed sufficiently
far from individual local neurons to prevent any particular cell from dominating
the electrophysiological signal. This signal is then low-pass filtered, cut off at
300Hz, to obtain the local field potential (LFP). The low impedance and
positioning of the electrode allows the activity of a large number of neurons to
contribute to the signal. The unfiltered signal reflects the sum of action poten-
tials from cells within approximately 50 350µm from the tip of the electrode
(Legatt et al. [14]).
The frequency of the LFP signals in corpus striatum will then be compared
with those appeared as the results of the numerical simulation of the averaging
transformation by given morphological properties.
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3.1. The Corpus Striatum
The neuronal populations of the striatum could be divided into four classes:
Spiny projection neurons (about 96% of the whole neural population) are GABAer-
gic neurons, which get external inputs from cortical areas, thalamus and sub-
stantia nigra pars compacta (Smith et al. [20]). These neurons also get inputs
from the dopaminergic, GABAergic and acetylcholinergic interneurons. Large
aspiny neurons (cholinergic), GABAergic interneurons and dopaminergic neu-
rons comprise the rest population of striatal neurons. The cholinergic interneu-
rons get external inputs from thalamus and substantia nigra pars compacta;
and internal inputs from the GABAergic interneurons. They project to the
dopaminergic and projection neurons. The action of the cholinergic interneu-
rons is assumed to have opposite effects on the action of the dopaminergic
neurons on the whole network. The cholinergic neurons inhibit the activity of
the projection neurons of the direct pathway (mostly D1system) and disinhibit
the activity of the indirect pathway neurons (D2system) (DiFiglia [7], Graybiel
et al. [12], DiFiglia et al. [5], DiFiglia and Carey [6], Gerfen [10], Betarbet et al.
[3], Flores-Hernandez et al. [9], Graveland et al. [11], Bennett and Wilson [2]).
A schematic representation of the microcircuitry of corpus striatum is shown in
Fig. 2.
MATLAB has been used to simulate the averaging across the network of
striatum. An overall number of 6400 neurons has been used for the simulation
of averaged potentials in striatum. The density distribution function ρis repre-
sented in Figure 3. The local and global connectivity function ψand χdefined
the necessary computational parameters based on Figure 2. We have induced
a single excitatory signal from cortical projection neurons to the cholinergic
neurons in striatum to simulate the simplest integration process.
It reveals that the activity transmission induced by a constantly activated
neurons is approximately radial and oscillatory. The activity of a single neuron,
forced by a constant input, produces activation-waves on the striatal populations
(Fig. 3).
Such neurons are simplified versions of the tonically active cholinergic in-
terneurons. Activations of neurons of other classes suggest similar activation
waves across the striatal populations. We observe that the simulated oscil-
lations of v(t) (50Hz) are qualitatively correlated with the LFP-studies of
basal ganglia which also suggest oscillations in control patients (Boraud et al.
[4]). The efficiency of the averaging transformation has been also investigated
for other brain compartments. In general, the averaged potentials of the com-
partments reveal oscillatory dynamical behaviour. For example, synchronized
gamma oscillations were observed in the globus pallidus. The simulation results
for the globus pallidus could be well reproduced by the reader using the aver-
aging transformation. Therefore, the representation of these results is omitted
in the present study.
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Figure 2: Schematic ultrastructural morphology of the primate’s striatum, including the neu-
rochemical synaptology. The green/orange arrows denote inhibitory/excitatory afferents. The
dashed arrows are external efferents to the striatal neurons. Hereby, St1Aand St1Bdenote
the spiny projection neurons which project to Globus Pallidus externa and Globus Pallidus
interna. St2denotes the dopaminergic interneurons, St3the GABAergic interneurons, and
St4the acetylcholinergic neurons.
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Figure 3: Left: The distribution of striatal interneurons based on experimental data. Right:
The oscillatory dynamics of the activity of striatal neurons by a single constant activation
with a realistic spatial distribution of the neurons (tonically active cholinergic neurons). The
light nodes denote active neurons.
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4. Discussion
In conformance with LFP experiments, the multiscale averaging operator (1)
transforms the synaptic potentials along the network structure of brain region
such as corpus striatum to local field potentials of the same frequency range.
This represents a first step from the neuroscience at Hodgkin-Huxely dimension
to the system biological level of consideration. Although this work was initially
inspired by one of the most intriguing problems of computational neuroscience,
it appears to be appropriate for several other intriguing applications. The char-
acterization of the discrete fundamental domains in a complex network in terms
of n-cells which is one of the dominating concepts of this mathematical ap-
proach, provides the possibility of the multiscale transformations of information
along discrete structure that are continuously realized. Beside the advantages of
this model such as its agreement with electrophysiological experiments, further
computational investigations are needed to verify its validity for more complex
systems.
Acknowledgment.. The financial support by the Interdisciplinary Center for Sci-
entific Computing and the International Graduiertenkolleg 710 (DFG) and the
funding by National Genome Research Network are acknowledged.
Appendix..
Neurotransmitter -Neurotransmitters are the most common class of chem-
ical messengers in the nervous system;
Synapse-Chemical synapses are specialized junctions through which neu-
rons signal to each other and to non-neuronal cells such as those in muscles.
Chemical synapses allow neurons to form circuits within the central ner-
vous system. They are crucial to the biological computations that underlie
perception and thought;
Morphology-The term morphology in biology refers to form, structure and
configuration of an organism. This includes aspects of the outward appear-
ance (shape, structure, colour, pattern) as well as the form and structure
of the internal parts like bones and organs;
Ultrastructural morphology-Cell and tissue morphology in the electron-
microscope level;
Interneuron-An interneuron (also called relay neuron, association neuron
or local circuit neuron) is a multipolar neuron which connects afferent
neurons and efferent neurons in neural pathways. Like motor neurons,
interneuron cell bodies are always located in the central nervous system;
Golgi method-Golgi’s method is a nervous tissue staining technique;
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Immunohistochemical studies -Immunohistochemistry or IHC refers to the
process of localizing proteins in cells of a tissue section exploiting the
principle of antibodies binding specifically to antigens in biological tissues;
References
[1] N . M. Avena, P. Rada, B. G. Hoebel, Evidence for sugar addiction:
Behavioral and neurochemical effects of intermittent, excessive sugar
intake, Neurosci. Biobeh. Rev. 32 (2008) 20-39.
[2] B. D. Bennett, and C. J. Wilson, Synaptology and physiology of neos-
triatal neurones. In: Brain dynamics and the striatal complex (Miller
R, Wickens J, eds), London, Harwood Academic, 2000.
[3] R. Betarbet, R. Turner, V. Chockkan, M. R. DeLong, K. A. Allers, J.
Walters, A. I. Levey, J. T. Greenamyre, Dopaminergic neurons intrinsic
to the primate striatum, J Neurosci. 17(17) (1997) 6761-6768.
[4] T. Boraud, P. Brown, J. A. Goldberg, A. M. Graybiel, P. J. Magill,
: Oscillations in the basal ganglia: The good, the bad, and the unex-
pected, The Basal Ganglia VIII (2005) 3-25.
[5] M. DiFiglia, P. Pasik, T. Pasik, A Golgi study of neuronal types in the
neostriatum of monkeys, Brain Res. 114(2) (1997) 245-256.
[6] M. DiFiglia, and J. Carey, Large neurons in the primate neostriatum ex-
amined with the combined Golgi-electron microscopic method, J Comp
Neurol. 244(1) (1986) 36-52.
[7] M. DiFiglia, Synaptic organization of cholinergic neurons in the monkey
neostriatum, J Comp Neurol. 255(2) (1987) 245-258.
[8] W. E, and B. Engquist, The heterogeneous multi-scale methods,
Comm. Math. Sci. 1 (2003) 87-133.
[9] J. Flores-Hernandez, E. Galarraga, J. Bargas, Dopamine selects gluta-
matergic inputs to neostriatal neurons, Synapse 25 (1997) 185-195.
[10] C. R. Gerfen, Synaptic organization of the striatum, J Electron Microsc
Tech. 10(3) (1988) 265-281.
[11] G. A. Graveland, R. S. Williams, M. DiFiglia, A Golgi study of the
human neostriatum: neurons and afferent fibers, J Comp Neurol. 234(3)
(1985) 317-333.
[12] A. M. Graybiel, V. M. Pickel, T. H. John, D. J. Reis, C. W. Ragsdale
Jr., Direct demonstration of a correspondence between the dopamine is-
lands and acetylcholinesterase patches in the developing striatum, Proc
Natl Acad Sci U S A 78(9) (1981) 5871-5875.
10
Nature Precedings : hdl:10101/npre.2009.3348.1 : Posted 19 Jun 2009
[13] H. Haken, Synergetics: Introduction and Advanced Topics (Physics and
Astronomy Online Library), Springer, 2004.
[14] A. D. Legatt, J. Arezzo, and H. G. Vaughan Jr., Averaged multiple
unit activity as an estimate of phasic changes in local neuronal activity:
effects of volume-conducted potentials, J Neurosci. Meth. 2(2) (1980)
203-217.
[15] S. A. Levin, and D. Chao, Herding behaviour: The emergence of large-
scale phenomena from local interactions, Diff. eq. with. appl. Biol.
Fields institute communications, AMS (1999) 81-96.
[16] M. Parent, A. Parent, The microcircuitry of primate subthalamic nu-
cleus, Parkinsonism Relat Disord. 13 Suppl 3 (2007) 292-295.
[17] G. A. Pavliotis, and A. M. Stuart, Multiscale Methods: Averaging and
Homogenization, Springer, 2008.
[18] P. Rada, K. Jensen, B. G. Hoebel, Effects of nicotine and
mecamylamine-induced withdrawal on extracellular dopamine and
acetylcholine in the rat nucleus accumbens, Psychopharm. 157 (2001)
105-110.
[19] P. Rada, D. F. Johnson, M. J. Lewis , B. G. Hoebel, In alcohol-
treated rats, naloxone decreases extracellular dopamine and increases
acetylcholine in the nucleus accumbens: evidence of opioid withdrawal,
Pharm. Biochem. Behavior 79 (2004) 599-605.
[20] Y. Smith, M. D. Bevan, E. Shink, J. P. Bolam, Microcircuitry of the
direct and indirect pathways of the basal ganglia, Neuroscience. 86(2)
(1998) 353-387.
[21] J. R. Wickens, R. Kotter, M. E. Alexander, Effects of Local Connectiv-
ity on Striatal Function: Simulation and Analysis of a Model, Synapse
20 (1995) 281-298.
11
Nature Precedings : hdl:10101/npre.2009.3348.1 : Posted 19 Jun 2009
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