Workshop 3: Dynamical Systems and Data Analysis in Neuroscience: Bridging the Gap

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  Inferring Dynamics of Neurons from Field Potentials in the Auditory Brainstem
  Joshua Goldwyn

  Membrane potential (Vm) is the standard representation of neural activity at the single-cell level. Vm represents the difference between intracellular voltage and extracellular voltage (Vm = Vi-Ve), where extracellular voltage (Ve) is generated by the combined activity of many neurons. I will explore the connection between these cell-level and population-level signals. I use a combination of mathematical modeling and data analysis to draw insights regarding the dynamics of neurons and synaptic currents in the auditory brainstem. In addition, I use simulations to show that extracellular voltage -- often thought of as a byproduct of neural activity -- may in fact modulate neural activity and influence neural computations.

  
  

  This work is in collaboration with John Rinzel (New York University) and the Laboratory of Auditory Neurophysiology at the University of Leuven (director: Philip Joris)

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  Explanation of variability in data through optimal transport
  Esteban Tabak

  A methodology based on the theory of optimal transport is developed to attribute variability in data sets to known and unknown factors and to remove such attributable components of the variability from the data. Denoting by $x$ the quantities of interest and by $z$ the explanatory factors, the procedure transforms $x$ into filtered variables $y$ through a $z$-dependent map, so that the conditional probability distributions $
  ho(x|z)$ are pushed forward into a target distribution $mu(y)$, independent of $z$. Among all maps and target distributions that achieve this goal, the procedure selects the one that minimally distorts the original data: the barycenter of the $
  ho(x|z)$.
  
  We will discuss the relevance of this methodology to medicine and biology, including the amalgamation of data sets and removal of batch effects, the analysis of time series, the analysis of dependence among variables and the discovery of previously unknown variability factors.

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  Attractor dynamics in the navigation system
  Adrien Peyrache

  The head-direction (HD) system functions as a compass, with member neurons robustly increasing their firing rates when the animal’s head points in a specific direction. HD neurons may be driven by peripheral sensors or, as computational models postulate, internally generated (attractor) mechanisms. We addressed the contributions of stimulus-driven and internally generated activity by recording ensembles of HD neurons in the antero-dorsal thalamic nucleus and the post-subiculum of mice by comparing their activity in various brain states. The temporal correlation structure of HD neurons was preserved during sleep, characterized by a 60°-wide correlated neuronal firing (activity packet), both within and across these two brain structures. During rapid eye movement sleep, the spontaneous drift of the activity packet was similar to that observed during waking and accelerated tenfold during slow-wave sleep. These findings demonstrate that peripheral inputs impinge on an internally organized network, which provides amplification and enhanced precision of the HD signal.

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  Temporal patterns of intermittent neural synchronization
  Leonid Rubchinsky

  Synchronization of neural activity in the brain is involved in a variety of brain functions including perception, cognition, memory, and motor behavior. Excessively strong, weak, or otherwise improperly organized patterns of synchronous oscillatory activity appear to contribute to the generation of symptoms of different neurological and psychiatric diseases. However, neuronal synchrony is frequently not perfect, but rather exhibits intermittent dynamics. So the same synchrony strength may be achieved with markedly different temporal patterns of activity (roughly speaking oscillations may go out of the synchronous state for many short episodes or few long episodes). I will discuss this situation from two perspectives: the phase-space perspective and associated considerations of dynamical systems theory and time-series analysis perspective. I will then proceed with the application of this analysis to the neurophysiological data in healthy brain, Parkinson's disease, and in drug addiction disorders.

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  Fragility in the human decision making system: when irrationality hijacks logic
  Sridevi Sarma

  Decision-making links cognition to behavior and is a key driver of human personality, fundamental for survival, and essential for our ability to learn and adapt. It has been well established that humans make logical decisions where they maximize an expected reward, but this rationality is influenced by their internal biases (e.g. emotional state, preferences). Psychiatric patients who have dysfunctional cognitive and emotional circuitry frequently have severe alterations in decision-making. Unfortunately, the function of relevant neural circuits in humans is largely uncharted at fine temporal scales, severely limiting the understanding of changes underlying disruption associated with age or psychiatric diseases. In this study, we localize neural populations, circuits, and their temporal patterns on a millisecond scale that are critically involved in human decision-making.

  
  

  Twelve human subjects, implanted with multiple depth electrodes for clinical purposes, performed a gambling task while we recorded local field potential neural activity from deep and peripheral brain structures. We propose a dynamical system model to explain the individual variability in decision making. We then identify neural correlates of model variables. Our models suggest a spectrum of decision-makers that range from irrationally to logical, and analyses of the neural data suggest that, specific oscillations in brain structures, including anterior insula, amygdala and cingulate cortex are shown to influence betting behavior (what you bet and how quickly you make the bet) in a profound way. These findings provide new insight into how humans link their internal biases (e.g. emotions) to decisions.

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  Building bridges between model and experiment to obtain an essence of theta rhythm generation
  Frances Skinner

  Oscillatory activities are hallmarks of brain output that are linked to normal and pathological functioning. Thus, determining mechanisms for how brain oscillations are generated is essential. However, the multi-scale, nonlinear nature of our brains makes them highly challenging to understand. In particular, theta oscillations (3-12 Hz) were discovered almost 80 years ago and are one of the most robust oscillations in the brain, including the hippocampus where they are associated with exploration. Although several cellular-based network models of varying levels of complexity have been developed, it is still unclear how theta oscillations are generated in the hippocampus. In this talk, I will describe the development of our cellular-based network models where we have taken advantage of an *in vitro* whole hippocampus preparation that spontaneously generates theta rhythms. Using theoretical insights and biological constraints, our developed models can produce theta rhythms, thus suggesting the underlying essence of their generation.

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  Introduction: Interplay of data and models
  Leslie Kay

  TBD

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  Model-based Observation and Control for the Brain: From Control of Seizures and Migraines, to Reducing Infant Brain Infections in Africa
  Steven Schiff

  Since the 1950s, we have developed mature theories of modern control theory and computational neuroscience with little interaction between these disciplines. With the advent of computationally efficient nonlinear Kalman filtering techniques (developed in robotics and weather prediction), along with improved neuroscience models that provide increasingly accurate reconstruction of dynamics in a variety normal and disease states in the brain, the prospects for synergistic interaction between these fields are now strong. I will show recent examples of the use of nonlinear control theory for the assimilation and control of single neuron and network dynamics, a control framework for Parkinson’s disease, and the potential for unification in control of spreading depression and seizures. Recent results help explain why the subtle and deep intersection of symmetry, in brains and models, is important to take into account in this transdisciplinary fusion of computational models of the computational brain with real-time control. Lastly, I will describe how such symmetries apply to network optimization and control for the prevention of infant brain infections in Africa.

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  Allen Brain Observatory: 2P Calcium Imaging Inference
  Kyle Lepage

  As a portion of the Allen Brain Observatory, a major initiative at the Allen Institute for Brain Science, head fixed adult mice are shown both artificial and natural visual stimuli while high-throughput 2- photon calcium imaging data are recorded from the mouse visual cortex, allowing assessment of stimulus processing across cortical layers, cortical areas, and Cre lines. In support of this effort, to assess the accuracy of statistical inference, cell-attached electrophysiological (ephys) data are collected simultaneously with two-photon calcium imaging (ophys). This latter experiment reveals, particularly when imaging at the lower magnification required to cover the mouse cortex, that a large number of spikes are not represented by the fluorescence signal, and conversely, an upward transient in the fluorescence signal does not always correspond with the occurrence of a neuron action potential. Despite considerable methodological effort, it remains a challenge to associate fluorescence signal with neural spiking. In this presentation, I will describe a a three-part approach to estimate neural receptive- fields and filters: (i) generalized linear models of spiking are estimated directly from fluorescence signal without direct knowledge of spike times, (ii) methods of estimation make explicit use of the calcium moments to facilitate (iii) the incorporation of calcium models derived from the joint ephys/ophys experiment.

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  Sequences of attractor-like states and the prediction of consumption behavior in single trials
  Don Katz

  Neural responses to taste administration are highly dynamic—single-neuron responses reflect first taste presence, then taste identity, and then taste palatability (an experience-dependent variable that is intimately tied to consumption/rejection decisions), all within the first second following administration. Our ensemble analysis reveals the firing-rate transitions between these response “epochs� to be precipitous, near-instantaneous, and coherent across populations of simultaneously-recorded cortical neural ensembles; the sequence of attractor-like population states is highly reliable, but the timing of any particular transition varies from trial to trial. Furthermore, the onset of the late, palatability-related state provides a high-quality prediction of decision-related behavior (the latency of which also varies widely from trial to trial). Together, our data reveal a dynamical characterization of the taste system in action.

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  Data Assimilation for Verifying Models of Neurons and Networks
  Henry Abarbanel

  Using data assimilation tools built via methods of statistical physics, we discuss +ideas and applications to experimental data for estimating properties of Hodgkin-Huxley models of individual neuron biophysics. The experimental data comes primarily from nucleus HVC of the avain song production system.

  
  

  We then discuss new tools for the analysis of networks of neurons using extracellular recordings and results from the theory of electrostatics.

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  Inferring synaptic conductances from spikes using a biophysically inspired extension of the Poisson generalized linear model
  Jonathan Pillow
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  Statistical neuronal models: an overview
  Uri Eden, Mark Kramer