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Super-selective reconstruction of causal and direct connectivity with application to in-vitro iPSC neuronal networks

30 Apr 2020-bioRxiv (Cold Spring Harbor Laboratory)-

TL;DR: A novel mathematically rigorous, model-free method to map effective - direct and causal - connectivity of neuronal networks from multi-electrode array data and is shown to offer important insights into the functional development of in-vitro iPSC-derived neuronal cultures.

AbstractDespite advancements in the development of cell-based in-vitro neuronal network models, the lack of appropriate computational tools limits their analyses. Methods aimed at deciphering the effective connections between neurons from extracellular spike recordings would increase utility of in-vitro lo- cal neural circuits, especially for studies of human neural development and disease based on induced pluripotent stem cells (hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fundamentally unable to correctly identify indirect and apparent connections between neurons, generating redundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe a novel mathematically rigorous, model-free method to map effective - direct and causal - connectivity of neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical and deterministic indicators which, first, enables identification of all existing functional links in the network and then, reconstructs the directed and causal connection diagram via a super-selective rule enabling highly accurate classification of direct, indirect and apparent links. Our method can be generally applied to the functional characterization of any in-vitro neuronal networks. Here, we show that, given its accuracy, it can offer important insights into the functional development of in-vitro iPSC-derived neuronal cultures by reconstructing their effective connectivity, thus facilitating future efforts to generate predictive models for neurological disorders, drug testing and neuronal network modeling.

Summary (4 min read)

1. Introduction

  • In-vitro cultures of primary neurons can self-organize into networks that generate spontaneous patterns of activity [10, 74, 58], in some cases resembling aspects of developing brain circuits [37, 24].
  • These methods estimate the effective connectivity of a measured neuronal network by explicitly modeling the data generation process, i.e. only the connectivity of a simulated network model is inferred without any theoretical guarantee about its accuracy and its ability to correctly estimate the connectivity of the biological network [14, 76].
  • Moreover, as the partial correlation matrix is symmetric, this method is not useful for detecting the causal direction of neuronal links.
  • The authors show an experimental application of their approach to spontaneously generated in vitro networks of human iPSC-derived neurons cultured on MEAs providing an analysis and interpretation of the physiology not possible otherwise.

2. Materials and Methods

  • The core of their methodology is graphically described in Figure 2 and includes three main phases: 1. statistical, correlationbased reconstruction of functional connectivity; 2. mathematically-rigorous super-selection of direct links via identification of peaks related to indirect and apparent links and 3.
  • The algorithm constructs correlation triangles by considering all possible combinations of correlation delays for any possible triplet of neurons .
  • The super-selection rule is formally presented later.
  • Importantly, the algorithm removes correlations from the analysis, but does not remove inferred physical connections.

Temporal correlations

  • (2) Using the Fast Fourier Transform (FFT) and the correlation theorem, computing correlations in Eq. (1) can be efficiently performed in O(S log(S)) with S the number of samples composing the signals sj .
  • Their amplitude can be regarded as a measure of the level of correlation between the spikes in their registered firing activities.
  • The higher the amplitude of a peak in Rjk(τ) (if any), the higher the probability that there is a statistical dependency between neuron j and neuron k.
  • As explained earlier in the text, the existence of a functional coupling between two neurons does not necessarily imply that there is an effective connection between them.
  • The location of each correlation peak with respect to the origin indicates the temporal delay τpeakjk between the activity of neuron j and neuron k .

Peak detection

  • The authors implemented a peak detection algorithm applied to Rjk(τ) to identify all existing functional correlations between any pair of neurons (j, k) in the network and to discern the directional dependency between their spiking activities.
  • As introduced above, the authors assume that a correlation peak in Rjk(τ) represents a potential connection between j and k and that τpeakjk is the signal propagation delay between them.
  • The definition of “near-perfect match” is based on the choice for the parameter which represents the acceptable degree of temporal approximation when computing Eq. 5.
  • The algorithm aims to construct njk × nkm × nmj correlations triangles given by all possible combinations of correlation peaks of any triplet of neurons’ pairs .
  • Within this framework, each correlation triangle shares up to three edges with G, and the union E′ of all τhjk defines the direct graph G ′ = (V,E′).

Edge covering minimization

  • Therefore, the challenge is to find a discrimination rule that allows us to select the correct τhjk in the correlation triangles that satisfy Eq. (4) (or Eq. (5)).
  • The larger the variation of the delayed timing between the input and the output neurons, the larger the phase noise in the associated correlation peak which will have smaller amplitude and larger standard deviation than the correlation among neurons with input and output signals without phase noise and perfectly synchronized.
  • To clarify this point, let’s consider the example reported in Figure 4.
  • If the authors consider the triangles ACD or ABD as in Figure 4, in both cases, the delay τDA is the one detected and discarded because, as explained in Figure 3, the corresponding correlation peak has lower amplitude and larger width as it results from a signal that has propagated through three links.
  • Within this picture, the authors can establish the second step in the super-selection algorithm as: Given a correlation triangle (τhjk, τ h′ km, τ h′′ mj), the delay associated with the smallest correlation peak am- plitude min(Ahjk, A h′ km, A h′′ mj) (8) estimates the false positive connection and is discarded from E′.

Connectivity matrix reconstruction

  • There are three fundamental parameters that affect the inference performance of this method: T defines the time window (−T,+T ) over which to search for correlation peaks in the correlation function Rjk. σ is important because the location of the detected correlation peaks weakly depends on it.
  • Large values increase the number of detected correlation peaks and computed correlation triangles with the potential shortcoming that true positive connections are filtered out.
  • This process allowed us to individuate a range of values for T and σ where the inference performances of the algorithm reached a maximum plateau (Fig. 6D), and define the reconstruction rule of their connectivity method as follows (the numerical details are discussed in the next section of Materials and Methods).
  • On the other hand, the maximum value for T can be chosen as several times (for example 5-6) the average delay among neurons in order to include more correlation triangles later used to refine the selection.

Experimental methodology

  • To develop and validate their connectivity method the authors used spiking data generated via simulations of neuronal networks based on the Izhikevich model [29] (see Supplementary Material and Fig. S2).
  • The original code was modified to guarantee high levels of activity in the network as well as bursting like behavior similar to that registered in their experiments .
  • It is worth noting that their model is general and not restricted to sparse connectivity.
  • For each network size, 20 different networks were randomly generated, simulated and then analyzed for connectivity reconstruction.

Performance measures

  • The performances were assessed based on the indicators TP/Nc (net number of true positive (TP) connections, with Nc the number of connections in the simulated neuronal network), FP/Nc (net number of false positive (FP) connections) and ∆ = (TP − FP )/Nc (confidence indicator).
  • ∆ is independent on the connectivity of the network being reconstructed and, because of its definition, it better defines the level of confidence in the detection of TPs by highlighting the method capabilities in rejecting or not the false positive connections.
  • For the sake of comparison with the literature, the authors also used the more standard Accuracy measure ACC = (TP + FP )/Ntot [49, 19].

Numerical experiments

  • This allowed us to isolate the activity of a few units per electrode, which resulted in the reconstruction of the activity of multiple detected neurons in the MEA well .
  • In a few cases, the clustering approach did not perform efficiently and generated either too many or too few clusters which were detected by observing the increased number of outliers in the spike sorting output.
  • For σ, observations on the recordings and the level of smoothing required for high-frequency noise removal led us to select σ ∈ (0.3, 0.8) ms.
  • The authors calculated the average in-degree and out-degree of the vertexes of each directed graph corresponding to a reconstructed network by calculating all incoming and outgoing connections for each network vertex and then averaging over the total number of vertexes per network.

Numerical results

  • To evaluate the performances of their method, the authors built a numerical model by designing and simulating an integrate-and-fire neuronal network mimicking the activity of in vitro cultures of neurons (see Supplementary Material).
  • As a result, the same false positive connections observed for a given pair of neurons are very unlikely detected by many different points, and at high frequency they are filtered out.
  • For two given points p1 and p2 the algorithm detected 15% and 20% FPs, respectively; however, most of the FPs detected by point p1 did not correspond to the ones detected by point p2.
  • Since the authors made the hypothesis that each node in the network model has the same average connectivity (preserved in- and out-degree) which does not increase with the network’s size, they do not expect and they are not interested in seeing connectivity dependent variations.
  • The authors also studied the integration and segregation properties of cultured human iPSC-derived neural networks (9C).

Discussion

  • The authors demonstrated a new model-free based approach to infer effective - active, direct and causal - connections from in vitro neuronal networks recorded on MEAs.
  • In terms of scalability, their algorithm matches the scalability properties of most of the state-of-the-art connectivity methods which, being based on pairwise statistical and correlation studies, scale with a practical computational complexity of the order of O(n2), where n is the number of neurons.
  • More specifically, the authors have three main routines whose complexity should be assessed: the computation of pairwise correlations, the peak detection algorithm, and the detection of false positive connections.
  • When applied to biological networks, their reconstruction method assumes that the spike sorting is accurate enough to separate the most prominent contributions in the activity of the network.
  • High density MEAs that include tens of thousands of electrodes at cellular and subcellular resolution [73, 80, 38, 7], and complementary voltage and calcium imaging approaches [26, 41, 3, 27] that provide useful information about the localization and classification of recorded neurons, offer optimized acquisition settings and will greatly improve the resolution and accuracy of their approach.

4. Conclusions

  • The authors have presented an innovative approach to map the effective connectivity of neural networks from multielectrode array data.
  • Notably, their connectivity algorithm succeeds in detecting direct connections between neurons through a mathematically rigorous selection scheme that distinguishes between apparent or non-direct links and direct ones, therefore enabling inference of directed causal relationships between connected neurons.
  • Furthermore, it will be broadly applicable to experimental techniques for neural activation and recording, increasing its utility for the analyses of spontaneous neural activity patterns, as well as neuronal responses to pharmacological perturbations and electrical and optogenetic stimulations [70, 26, 38, 41, 3].
  • The authors thank Fabio L. Traversa for fruitful and constructive discussions on the theoretical framework.
  • D.P. and A.B. designed and organized the experimental studies.

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Super-selective reconstruction of causal and direct connectivity with
application to in-vitro iPSC neuronal networks
Francesca Puppo
a,
, Deborah Pr´e
b,
, Anne Bang
b,∗∗
, Gabriel A. Silva
c,∗∗
a
BioCircuits Institute, Center for Engineered Natural Intelligence, University of California, San Diego, La Jolla, 92093 CA,
USA
b
Conrad Prebys Center for Chemical Genomics, Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037,
USA
c
Department of Bioengineering, Department of Neurosciences, BioCircuits Institute, Center for Engineered Natural
Intelligence, University of California, San Diego, La Jolla, 92093 CA, USA
Abstract
Despite advancements in the development of cell-based in-vitro neuronal network models, the lack of ap-
propriate computational tools limits their analyses. Methods aimed at deciphering the effective connections
between neurons from extracellular spike recordings would increase utility of in-vitro local neural circuits,
especially for studies of human neural development and disease based on induced pluripotent stem cells
(hiPSC). Current techniques allow statistical inference of functional couplings in the network but are fun-
damentally unable to correctly identify indirect and apparent connections between neurons, generating re-
dundant maps with limited ability to model the causal dynamics of the network. In this paper, we describe
a novel mathematically rigorous, model-free method to map effective - direct and causal - connectivity of
neuronal networks from multi-electrode array data. The inference algorithm uses a combination of statistical
and deterministic indicators which, first, enables identification of all existing functional links in the network
and then, reconstructs the directed and causal connection diagram via a super-selective rule enabling highly
accurate classification of direct, indirect and apparent links. Our method can be generally applied to the
functional characterization of any in-vitro neuronal networks. Here, we show that, given its accuracy, it can
offer important insights into the functional development of in-vitro iPSC-derived neuronal cultures.
Keywords: neuronal network, effective connectivity, functional connectivity, apparent connectivity,
correlation, MEA, iPSC, development
1. Introduction
In-vitro cultures of primary neurons can self-organize into networks that generate spontaneous patterns
of activity [10, 74, 58], in some cases resembling aspects of developing brain circuits [37, 24]. The emer-
gent functional states exhibited by these neuronal ensembles have been the focus of attention for many
years [15, 83] as they can be used to investigate principles that govern their development and maintenance
These two authors contributed equally
∗∗
Corresponding authors
Email addresses: email: abang@SBPdiscovery.org (Anne Bang), email: gsilva@ucsd.edu (Gabriel A. Silva)
Preprint submitted to Elsevier January 25, 2021
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 27, 2021. ; https://doi.org/10.1101/2020.04.28.067124doi: bioRxiv preprint

[35, 44] and to produce biological correlates for neural network modeling [11, 66]. The introduction of hu-
man induced-pluripotent stem cell (hiPSC) technologies [69, 82] opened the possibility to generate in-vitro
neuronal networks in typical [30, 42], as well as patient-specific genetic backgrounds [57, 5, 75, 78, 8, 39],
demonstrating the potential to reproduce key molecular and pathophysiological processes in highly con-
trolled, reduced, experimental models that enables the study of neurological disorders and the discovery and
testing of drugs, especially in the context of the individual patient [72, 16, 61].
One common approach to obtain information from in vitro neuronal networks is to record their activity
via multi-electrode array (MEA) or calcium fluorescence imaging and then use network activity features to
describe their physiology. One main limitation, however, is that these high-dimensional data, which report
about the information representation in the network, do not translate into a clear understanding of how this
representation was produced and how it emerged based on neuronal connectivity [14]. The synchronization
of spontaneous spike trains among different MEA sites or neurons, also referred to as network bursting, is an
example of observed neural behaviors widely reported in the literature. The generation of network bursting
in an in vitro neuronal culture is evidence that the neurons are synaptically connected. However, the extra-
cellular nature of the MEA recording does not provide information about how neurons are connected and
how signals propagate between them, such that computational analyses are necessary to reconstruct their
complex dynamic patterns and relate their emergence to the underlying wiring diagram [66]. However, this
kind of analysis presents several challenges as it requires not only identification of functional relationships
between cells, but also reconstruction of the dynamic causality (i.e., the knowledge of which neuron fires first
and affects another one) between directly linked neurons that are simultaneously involved in several differ-
ent signaling pathways. This defines the difference between functional and effective connectivity inference:
the first only reports about statistical dependencies between cells’ activities without giving any information
about specific causal and direct effects existing between two neurons [76]; the second attempts to capture a
network of effective - direct and causal - effects between neural elements [65].
Only model-based approaches [14, 34] have been proposed for inference of effective connectivity. Among
them, dynamic causal modeling (DCM) [18] and structural equation modeling [36] variants have shown best
performances. However, these methods estimate the effective connectivity of a measured neuronal network
by explicitly modeling the data generation process, i.e. only the connectivity of a simulated network model
is inferred without any theoretical guarantee about its accuracy and its ability to correctly estimate the
connectivity of the biological network [14, 76].
Because of this limitation, descriptive, model-free approaches are usually preferred as they are easy to
implement, rely on a limited number of assumptions that are directly related to the investigated neuronal
network, and can be more easily validated [14, 34]. A number of model-free methods proposed for recon-
structing the connectivity of in vitro neuronal networks [19] have been previously reviewed [48] and tested
2
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 27, 2021. ; https://doi.org/10.1101/2020.04.28.067124doi: bioRxiv preprint

[76]. However, because they rely on purely statistical indicators, they can only infer how neurons are func-
tionally coupled, but lack the ability to identify the network of effective interactions between neurons by
either missing the directionality or confounding indirect and apparent links from direct ones. Directional-
ity conveys the causality of signaling in the network, i.e. which neural element has causal influences over
another (Figure 1A(i)). However, causality does not imply a direct connection between two neurons. In
fact, a functional coupling between two neurons can be causal even though the two neurons are not directly
connected, and this may occur if there is a multi-neurons pathway between the two cells (indirect connec-
tion, Figure 1A(ii)), or if the connection detected between the two neurons is simply a mathematical artifact
resulting from the correlation of correlations generated by common inputs from other participating neurons
(apparent connection, Figure 1A(iii)) [17].
Methods such as correlation [53], coherence [25, 23, 12], mutual information [19, 22, 51], phase and
generalized synchronization [51, 2], and joint entropy [19] describe only statistical dependencies between
recorded neurons without carrying any information of causality or discriminating direct and indirect effects.
Techniques such as cross-correlation [19, 28], directed and partial directed coherence [1, 56], transfer en-
tropy [19, 28, 33] and Granger causality [21, 59] are examples of causal indicators as they provide inference
of directionality of dependence between time series based on time or phase shifts, or prediction measures.
However, because these operators rely only on pairwise statistical comparisons and treats pairs of neurons
independently, they show the same limitations when dealing with indirect connections and external inputs.
Only a few techniques can compete in the challenge of inferring the effective connectivity of a network.
Partial-correlation [19, 68], which takes into account all neurons in the network, showed best performance
in detecting direct associations between neurons and filtering out spurious ones [45]. The most significant
limitation of this solution is its high computational cost. Moreover, as the partial correlation matrix is
symmetric, this method is not useful for detecting the causal direction of neuronal links. It also does not
attempt to infer self-connections [14]. A combination of correlation and network deconvolution was used
by Magrans and Nowe [13] to infer a network of undirected connections with elimination of arbitrary path
lengths caused by indirect effects. However, this method also can not identify directions of connections and
the singular value decomposition of network deconvolution has an extremely high computational complexity
[45]. A convolutional neural network approach [54] showed the same limitations in computational complexity
and undetected self- and causal connections. Figure 1B graphically summarizes the inference capabilities of
the state-of-the-art connectivity methods as reported in [14, 76, 17, 2].
In this work, we propose a novel, mathematically rigorous method that uses a model-free approach (i.e.
does not depend on a set of underlying assumptions about the biology of participating cells) to decompose
the complex neural activity of a network into a set of numerically validated direct, causal dependencies
between the active component neurons that make up the network. First, the inference power of statistical
3
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The copyright holder for this preprintthis version posted January 27, 2021. ; https://doi.org/10.1101/2020.04.28.067124doi: bioRxiv preprint

approaches (signal-, network- and information theory- based) allows mapping the functional connectivity
of the network. Then, we propose a mathematically rigorous selection scheme that distinguishes between
apparent or non-direct links and direct ones, therefore enabling inference of direct causal relationships be-
tween connected neurons which more realistically describe the effective connectivity of the network (Figure 2).
We evaluate the performances of the proposed method on synthetic datasets generated through simulation
of an integrate-and-fire neuronal network mimicking the activity of in vitro cultures of neurons, and demon-
strate important improvements, relative to the state-of-the-art connectivity methods, to network inference
accuracy due to a deterministic component of our method capable of identifying false positive connections.
We show an experimental application of our approach to spontaneously generated in vitro networks of
human iPSC-derived neurons cultured on MEAs providing an analysis and interpretation of the physiology
not possible otherwise. We describe the temporal evolution associated with the connectivity and dynamic
signaling of developing hiPSC-derived neuronal networks, including increasing synchronized activity and
the formation of small numbers of hyper-connected hub-like nodes, as similarly reported by others [30, 8].
These results further support the performance quality of our approach and provide an example of how this
connectivity method can be used to characterize network formation and dynamics, thus facilitating efforts
to generate predictive models for neurological disease, drug discovery and neural network modeling.
2. Materials and Methods
Theoretical framework for connectivity reconstruction
The central contribution of this manuscript is in providing an innovative, computationally efficient,
and easy-to-apply method for decomposing the collective firing properties stored in the electrophysiological
recordings from neuronal networks on MEAs into direct (one-to-one) and causal (directional) relationships
between all participating neurons. We propose a multi-phase approach that identifies and discards any
correlation link that does not directly relate to a direct interaction between two cells. The core of our
methodology is graphically described in Figure 2 and includes three main phases: 1. statistical, correlation-
based reconstruction of functional connectivity; 2. mathematically-rigorous super-selection of direct links
via identification of peaks related to indirect and apparent links and 3. reconstruction of directed causal
connectivity between neurons.
1. The functional connectivity (statistical dependencies) of a network is computed via pairwise correla-
tion studies. Functional interactions between neurons are represented by correlation peaks and their
delays τ . The algorithm constructs correlation triangles by considering all possible combinations of
correlation delays for any possible triplet of neurons (Figure 2.1). Importantly, correlation triangles do
not refer to any three-neuron physical connection, sometimes referred to as “neural triangles” in the
4
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 27, 2021. ; https://doi.org/10.1101/2020.04.28.067124doi: bioRxiv preprint

literature [63, 55]. Here we define a correlation triangle as a mathematical object that our algorithm
uses to classify functional interactions based on all possible triplets of correlation delays that can be
formed in the network. Therefore, correlation triangles exploit the entire signal history of neurons in
order to determine the correlation peaks.
2. Correlation peaks associated with indirect or apparent links in corresponding correlation triangles are
discarded from the analysis by means of a mathematical super-selection rule which deterministically
classifies the type of dependence between each triplets of neurons (Figure 2.2). The super-selection
rule is formally presented later. Here, it can be summarized as follows. If a correlation triangle is
made up of three correlation delays that are the combination of one another, one of the component
correlation delays is either representative of an indirect link (Figure 1A(ii)) or of an apparent link
(Figure 1A(iii)); therefore, this correlation delay does not refer to an effective connection and must be
discarded. When the algorithm finds a correlation triangle which satisfies this condition, it deepens
into the classification of the involved correlation delays and selects the correlation peak to remove
based on the peak’s amplitude. For example, in Figure 2.2, the algorithm identifies an indirect link
between 1 and 3 (a multi-neuron pathway), and an apparent link between 1 and 3 (correlation due to
a common output). The correlation peaks corresponding to these links in the correlation triangles are
discarded from the analysis. Importantly, the algorithm removes correlations from the analysis, but
does not remove inferred physical connections.
3. Only when all correlation peaks between two neurons are discarded, the algorithm recognizes that a
specific interaction is only apparent and deletes the corresponding connection. For example, in Fig-
ure 2.3, there is no existing connection between neurons 1 and 3. The estimated effective connectivity
includes only direct links for (1, 2) and (2, 3): two connections with opposite directionality exist be-
tween neuron 1 and 2 because positive and negative correlation peaks are detected in R
1,2
(τ
1
1,2
and
τ
+1
1,2
); one link connects neuron 2 to neuron 3 as a result of the positive correlation peaks in R
2,3
(τ
+1
2,3
and τ
+2
2,3
).
The following sections describe the mathematical details of the developed technique. The connectivity
reconstruction algorithm and associated functions for performance evaluation were implemented in Matlab
and code is available online at https://github.com/fpuppo/ECRtools.git.
Reconstruction of functional connectivity
Temporal correlations
To identify the temporal correlations between the activity of all pairs of N recorded neurons j, k
{1, ..., N} in the network, we computed the pairwise correlation function between the corresponding signals
s
j
and s
k
R
jk
(τ) =
Z
s
j
(t)s
k
(t + τ )dt (1)
5
(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.
The copyright holder for this preprintthis version posted January 27, 2021. ; https://doi.org/10.1101/2020.04.28.067124doi: bioRxiv preprint

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In a recent Nature methods paper relating to “Brains in a petri dish”, the authors developed a new streamlined method for inducing pluripotent stem cells to form cortex-like organoids (Figure 1), which include neurons supported by network of glial cells. Authors used an in vitro neural differentiation approach, where human cortical spheroids (hCSs) are maintained in floating conditions on low-attachment plates with biweekly changes of regular serum-free media. This system can be easily maintained for up to 9 months in vitro. Thus, authors were able to create functional and realistic layers of neurons that talk to each other in complex networks. Figure 1 Generation of human cortical spheroids [Image courtesy of Dr. Pasca2] Figure 1 is the schematic representation of the main stages during the process of creation of hCS. Authors used low attachment plates for the suspended colonies. Authors used both BMP and TGF signaling pathways to achieve rapid and efficient neural induction. At 6th day, EGF was added and at 25th day, BDNF was added. Medium was changed very frequently. These hCS grew to 300 microns in diameter by 2 weeks of culture and then reached 45 mm in diameter by 2.5 months. To help characterize these hCS, the authors used many functional classification techniques2. They studied the functional characterization of the neurons by using fura-2 (calcium) imaging and panels of antibodies in the human fetal cortex. This system of 3D network was also amenable to slice physiology techniques. The authors performed whole cell recordings and found that almost 80% of the cells fired action potentials in response to depolarizing current steps. There have been other techniques used in the past for developing differentiating pluripotent stem cells into cortical neurons. Some examples include neural induction in high-density monolayer cultures, embedding clusters of hiPSCs in gelatinous protein mixtures (such as Matrigel) and later culturing them in a spinning bioreactor, using embryoid bodies derived from hiPSCs that are plated on coated surfaces to generate neural progenitors2,5–7. In 2013, Lancaster et. al. in order to recapitulate features of human cortical development, namely characteristic progenitor zone organization with abundant outer radial glial stem cells, developed cerebral organoids that had similar development as in human brain6. The authors also used these cerebral organoid to model microcephaly defect (which has been difficult in model in mice) that could help explain various disease phenotypes. In 2015, Maguruma and colleagues developed a method to generate neurons of the cerebellum by 3D culture of human embryonic stem cells with sequential addition of growth factors7. In the paper on Cortical Neurogenesis (complexity emerging from simplicity)5, authors modeled spatial and temporal patterns of corticogenesis (see figure 2). These 3 D models could recapitulate similarity to in-vivo organization of cortical structure. Following paragraphs talk about the potential applications of organoid for various disease models. Figure 2 Temporal and Spatial modeling cortical neuron neurogenesis [Image courtesy of Dr. Anderson5] Timothy syndrome (TS), a development delay disorder caused by a mutation in a L-type voltage-gated calcium channel, can cause autism. The iPSC derived cortical cells from TS patient led to revelation about defects in calcium signaling and neuronal activity, and defects in the generation of specific types of neurons8. Pluripotent stem cells were used to identify the lysosomal alterations in Gaucher disease (GD) neurons (genetic disease in which fatty substances accumulate in cells and certain organs). It was found that the lysosomal alterations described were caused by the GBA1-associated neurodegeneration9. Anand and his group have already taken the application of these corticoids to Alzheimer’s and Autism research1. Authors have filed an invention disclosure and are seeking an IP, so they were unable to disclose the methods. Figure 3 shows an image of an organoid. When, I asked the author about the potential of this work and timeline, his response was “Potential is enormous. The models will accelerate research and drug discovery and more accurately predict efficacy of drugs in human clinical trials, and a lot lower cost. Timelines will vary based on the subtype of a disease under consideration (most brain diseases and disorders are syndromes with different causes, though some may converge on a pathway)”. Figure 3 Image of an organoid [Courtesy of The Ohio State University1] Gulf War illness is considered to be the outcome of the use of organophosphate pesticides [permethrin (PM) and N,Ndiethyl-m-toluamide (DEET)], daily prophylactic anti-cholinesterase pyridostigmine bromide (PB), and stress. It is also shown to cause reduction of hippocampal column and brain gray matter. Organoid can be used to evaluate the pathobiology of these noxious chemical on human brain development.

2 citations


References
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Journal ArticleDOI
30 Nov 2007-Cell
TL;DR: It is demonstrated that iPS cells can be generated from adult human fibroblasts with the same four factors: Oct3/4, Sox2, Klf4, and c-Myc.
Abstract: SUMMARY Successful reprogramming of differentiated human somatic cells into a pluripotent state would allow creation of patient- and disease-specific stem cells. We previously reported generation of induced pluripotent stem (iPS) cells, capable of germline transmission, from mouse somatic cells by transduction of four defined transcription factors. Here, we demonstrate the generationofiPS cells from adult human dermal fibroblasts with the same four factors: Oct3/4, Sox2, Klf4, and c-Myc. Human iPS cells were similar to human embryonic stem (ES) cells in morphology, proliferation, surface antigens, gene expression, epigenetic status of pluripotent cell-specific genes, and telomerase activity. Furthermore, these cells could differentiate into cell types of the three germ layers in vitro and in teratomas. These findings demonstrate that iPS cells can be generated from adult human fibroblasts.

16,624 citations


"Super-selective reconstruction of c..." refers background in this paper

  • ...The introduction of human induced-pluripotent stem cell (hiPSC) technologies [12, 13] opened the possibility to generate in-vitro neuronal networks in typical [14, 15], as well as patient-specific genetic backgrounds [16, 17, 18, 19, 20, 21], demonstrating the potential to reproduce key molecular and pathophysiological processes in highly controlled, reduced, experimental models that enables the study of neurological disorders and the discovery and testing of drugs, especially in the context of the individual patient [22, 23, 24]....

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Journal ArticleDOI
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

16,520 citations


"Super-selective reconstruction of c..." refers methods in this paper

  • ...With the use of Matlab routines, we also computed the CCo as the fraction of triangles around a node, which is equivalent to the fraction of node’s neighbors that are neighbors of each other [61]....

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BookDOI
01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Abstract: Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.

15,308 citations


Journal ArticleDOI
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

14,541 citations


"Super-selective reconstruction of c..." refers background in this paper

  • ...Techniques such as cross-correlation [31, 41], directed and partial directed coherence [42, 43], transfer entropy [31, 41, 44] and Granger causality [45, 46] are examples of causal indicators as they provide inference of directionality of dependence between time series based on time or phase shifts, or prediction measures....

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Book ChapterDOI
01 Jan 2001
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.

10,077 citations


Frequently Asked Questions (2)
Q1. What are the contributions in "Super-selective reconstruction of causal and direct connectivity with application to in-vitro ipsc neuronal networks" ?

In this paper, the authors describe a novel mathematically rigorous, model-free method to map effective direct and causal connectivity of neuronal networks from multi-electrode array data. Here, the authors show that, given its accuracy, it can offer important insights into the functional development of in-vitro iPSC-derived neuronal cultures. 

In addition, it has good scaling capabilities and can be further generalized to any kind of network, thus allowing to target different problems in intact neurons, synthetic models as well as in vitro and in vivo systems. Furthermore, it will be broadly applicable to experimental techniques for neural activation and recording, increasing its utility for the analyses of spontaneous neural activity patterns, as well as neuronal responses to pharmacological perturbations and electrical and optogenetic stimulations [ 70, 26, 38, 41, 3 ]. As novel electrophysiology technologies come online and are validated, the methods the authors presented here will be in an immediate position to take advantage of them, resulting in fundamental improvements in spatial resolution and reconstruction accuracy. Furthermore, their algorithm can be further extended, improved, and possibly integrated with already in-use techniques to overcome important limitations such as the detection of inhibitory connections and the inference of effective connectivity in the bursting regime.