Setting

For Imaging to Connectivity

Figure 1: Neural cultures. We are studying methods to reconstruct the effective connectivity between neurons from observations of their activity. The activity is measured by imaging the calcium influx into neurons using fluorescent molecules. To experiment with these techniques, we use cultured neurons. The nethod is also applicable to slices of brain and to in vivo recordings of the surface of the brain after it has been surgically exposed.

Neuromorphic systems have been a long time inspiration for computational intelligence systems, which in turn help us gaining a better understanding of the brain, with the long term goal of furthering our understanding of intelligent systems in general. The understanding of the brain structure is a key element of the puzzle. Additionally, understanding alterations in brain structure caused by disease, is essential to accompany research on the treatment of epilepsy and Alzeimer's disease and other neuropathologies. However, at the neural level, recovering the exact wiring of the brain (connectome) including nearly 100 billion neurons, having on average 7000 synaptic connections to other neurons, is a daunting task. Traditional neuroanatomic methods of axonal tracing cannot scale up to very large networks.

Figure 2: Video of neural activity visualized with calcium fluorescence in a neuron culture.

To address this problem in a more effective way than conventional methods, we propose to employ new computational techniques. A nascent methodology based on optical imaging of neural activity allows us to monitor the activity of tens of thousands of neurons simultaneously. The idea is to reverse engineer the structure of neural networks given time series of neuron activity acquired from video data (Figure 2). The imaging of calcium influx into neurons provides an indirect but accurate measure of action-potential generation within individual neurons. The method uses fluorescent molecules that respond to the binding of calcium ions by changing their fluorescence properties (see Grienberger, 2013, for a review). The rapid progress in technology and the new data sharing culture (Milham, 2012) will soon make available to neuroinformatic scientists large databases of optical recordings of hundreds of thousands or millions of neurons, which they need to be ready to analyze. Today already, publicly available data include the recording of 80% of the 100,000 neurons of a zebrafish larva awaiting efficient computational methods to reconstruct the underlying network (Ahrens, 2013).

Figure 3: Network reconstruction of in vitro neural cultures imaged with fluorescent calcium imaging (Stetter et al, 2012). The white dots are real neuron cell bodies. The red arrows are effective connections recovered computationally from videos of neural activity.

Challenges in bioinformatics to reverse engineer gene networks such as DREAM and “SBV improver” do not have yet their parallel in neuroscience. We are organizing a challenge to stimulate the advancement of research on neural network structure reconstruction algorithms from neurophysiological data, including causal discovery methods. The challenge makes use of realistic simulations of real networks of neurons observed via calcium fluorescence recordings. The winning methods will be used to analyze real data recorded from in vitro cultures of neurons (Figures 1-3) and the proposed structure will be verified in part by experiments conducted in a wetlab. We hope to capitalize on the rapid improvements of optogenetics methods for shutting down or switching on neurons by shining laser light, which already allows stimulating up to 1000 neurons (see Rainer-Isacoff, 2013, for a review). This would allow us to check the connectivity of networks reconstructed from observational data by performing actual interventions.

Our challenge will make simulated optical recordings of neurophysiological data available to the community in a format that does not require detailed understanding of neurobiology and therefore will give an opportunity to computational intelligence scientists to make a contribution. Our simulated data (Stetter, 2012) includes variations in dynamical regimes. This switching dynamics is a major challenge to network reconstruction, since directed “effective” connectivity can be very different during bursting and inter-burst phases. It can bear a resemblance to the underlying anatomical synaptic connectivity only in selected dynamical regimes, in which causal influences reflect dominantly mono-synaptic interactions. In parallel, we are planning a companion challenge on cause-effect pairs in time series data, which will nicely complement the proposed challenge by benchmarking methods to determine the causal relationships in pairs of variables, including recordings of real neurons available in abundance in public repositories.

It is anticipated that our challenge will help advance the state-of-the-art in inferring the structure of directed networks of units in general, beyond the neural connectomics applications. The goal of this challenge is to infer directed connections (synapses) of neural networks from patterns of neural activity. Such an oriented network and can be thought of as a causal network. Neurons have complex temporal patterns of activity. The problem can therefore be thought of as a causal structure reconstruction problem from time series data. Other instances of such problems are found in genomics, climatology, epidemiology, engineering, and econometrics.

Effective topology

Although neuroanatomy is a very old science, connectomics is a relatively new, but fast emerging, field. If statistical knowledge about connectivity patterns has been long available (see e.g. Braitenberg-Schüz, 1991), the aim of connectomics is to derive the detailed structure of whole large-scale neural systems. The first complete nervous system wiring diagram was accomplished with the 300 cell nervous system of a model organism: C. Elegans, a nematode worm, in the 1980's. It was deduced from reconstructions of electron micrographs of serial sections (White, 1986). Partial connectomes for larger nervous systems including the fruit fly and the mouse have since been produced with a combination of neuroanatomical techniques (See, Seung, 2012, for a review). But even the most advanced techniques for labeling individual neurons with distinguishable colors via a method called Brainbow (Livet, 2007) require a difficult tracing of neuron ramifications, and the resolution of optical microscopes is insufficient to reliably visualize synapses. Electron microscopy provides sufficient resolution , but no color coding, and yields voluminous amounts of data that is being analyzed very slowly with a combination of informatics methods and human labor. In 2012, a Citizen science project called EyeWire began attempting to crowdsource this task through an interactive game.

Figure 4: Electron Microscopy. One (very laborious) way of establishing connectivity between neurons is to use election microscopy. This is a destructive approach that cannot be performed in vivo. Photo from BrainPreservation.org.

In this challenge, we consider another type of approach, which consists in reconstructing networks of interaction between neurons from patterns of activity to obtain an “effective topology”. Inferring network topology from patterns of neural activity is not new. There have been active research efforts in the recent years to produce and analyze connectomic databases at the mesoscale and macroscale level , based on non-invasive imaging techniques of brain activity such as functional magnetic resonance imaging (fMRI), including the Human Connectome Project, led by the WU-Minn consortium. At the cellular level, the effort of reconstructing networks from neural activity can be traced back to a 2006 paper, already using the terminology of "effective topology", where only the in-degree of a neuron was estimated based on the simple logic "higher firing frequency = more inputs". (Eytan-Marom, 2006). The first major study using calcium imaging identified "hub neurons" with a simple cross-correlation approach (Bonifazi, 2009). This was followed by a major contribution by the Paninski group at Columbia also aiming at reconstructing the connectivity from calcium fluorescence imaging data (Vogelstein, 2009; Mishchencko, 2011). The idea was to first infer spike times as a Bayesian inverse problem, and then infer the GLM kernels (representing synaptic weights) of the supposed GLM (generalized linear model) for the neurons. Their work builds on a rigorous study of GLM models demonstrating reconstruction of spike data (Truccolo, 2005). One criticism of the approach is that it was proven successful only with data generated with the same model as the model used for reconstruction. Real neurons are very diverse and an approach that is bound too tightly to a supposed model of the neurons may be plagued with artifacts. This motivated model-free network reconstruction techniques (Stetter, 2012; Orlandi 2013).

Effective topology reconstruction is not sensu stricto the same thing as establishing a map of “anatomically correct” structural connections (actual synapses) because of a variety of reasons, including:

1. Some anatomical connections may be missed by the reconstruction because:

• some synapses may be “dormant” (weak or inactive);
• some interactions may be invisible due to signal cancelation in feed-back circuits;
• two (or more) neurons may be overlapping and their signals merged.

2. Some spurious connections may be inferred because:

• some “effective” connections may be relayed by invisible neurons and not correspond to actual synapses;
• some “effective” connections may result from artifacts of network reconstruction algorithms, which rely on data limited in time resolution;
• some “effective” connections may reflect real influences mediated by collective network properties, rather than by pairwise interactions.

However, algorithmic reconstruction approaches are far more scalable than anatomical axonal tracing and the hope is that, with improvements in imaging techniques, informatics tools, and theoretical understanding of observed neural dynamics, it will become possible to unravel connectomes of the nervous systems of large organisms. This motivates our proposal.

We focus on reconstructing networks from so-called “observational data”, which means the recording of cells let to evolve according to their own dynamics, without intervention of the experimentalists. This is in contrast with “interventional data” obtained by stimulating neurons with external means (electrical, optical, or chemical). Forcing given network nodes to assume given states, disconnecting them from their natural influences from other network nodes, is the basis of the experimental methodology in causal inference. It is the only reliable way to unambiguously unravel causal relationships (directed network connections) from node activity. However, conducting proper interventional experiments is costly, technically difficult, and sometimes unethical or impossible. Optogenomics is one of the most promising methods because it offers the possibility of intervening simultaneously on hundreds of neurons. Optogenetic paradigms use genetic techniques to induce the expression of light-activated ion channels into a living organism such that focused shining of light can trigger action potentials in the targeted neurons. But, the apparatus is complicated and expensive. Additionally, intervening on neurons puts stress on them and cannot be done extensively without damaging them . For these reasons, algorithms that unravel neural network structures from purely observational data will remain important as standalone methods or in conjunction with interventions to prepare them or guide them. We believe that this is feasible, particularly because from the perspective of complex dynamical systems the distinction between “observational” and “interventional” data (as made in the causal discovery literature) is blurred by the fact that neural networks generate in a sense their own self-organized set of experimental interventions by spontaneously bursting. Nonetheless, it is our intention to also investigate how the methods developed by the participants using observational data can be validated or complemented using interventional data. This could lay the basis for a new challenge of neural structure reconstruction blending observational and interventional data.

References