Brent Doiron - US grants

Multi-electrode recording technology and voltage sensitive dyes allow researchers to probe the structure of correlated, stimulus-driven neural activity in groups of cells. However, the diversity of brain areas and stimuli make a complete sampling of these patterns and their effects impossible. Furthermore, the evidence of correlations in stimulus response is strong, yet its role in neural coding difficult to intuit. Therefore, a combined, predictive theory of correlation formation and impact is required. This challenge is approached in three stages. First, a general mathematical theory is developed that relates input correlations of a stochastic forcing to the output correlations of resultant spike trains. The underlying tools will be linear response, population density, and Monte-Carlo methods for the nonlinear stochastic differential equations of spiking neural circuits. Next, this theory is applied to a variety of neural models to quantify how neuron biophysics, morphology, and coupling influence input-output correlation transfer. Finally, information-theoretic analyses are performed to estimate the impact of spike train correlations on the encoding and propagation of sensory inputs in representative neural circuits. Throughout the project, the investigators will work with experimental collaborators to refine and test these predictions.

Understanding the mechanisms by which the nervous system represents and processes information is a fundamental challenge for mathematical biology. It has long been known that information is represented by the intensity of individual neurons' responses. However, new multi-neuron recording and brain imaging techniques are revealing that the information carried by neural tissue is much more (or much less) than the summed contributions of individual neurons. In other terms, the cooperative, correlated features of neural responses can be essential. This poses a pair of fundamental, but unresolved theoretical questions: What are the basic mechanisms by which correlated activity is generated and propagated through layers of neural tissue? What are the consequences for information processing in neuronal networks? The answers will, in stages, make predictions for ongoing neurobiological experiments. For instance, understanding the relation between correlations and neural coding stands to impact the design of neural prosthetics, which code motor and sensory signals via cortical, retinal, thalamic, and cochlear implants. From an alternative perspective, many neurological disorders, such as epilepsy and Parkinson's disease, involve excessive correlation in neural tissue--describing the genesis of correlations and its negative impact on neural coding will aid in designing appropriate treatments that ultimately reduce correlation in the nervous system. Along the way, graduate students involved in this research will receive training in a highly interdisciplinary field, and will gain a broad perspective on mathematical neuroscience through regular visits between three research groups in different regions of the United States. The active involvement of the investigators in undergraduate research and course development will provide an opportunity to translate the questions addressed here into compelling educational topics on the cooperative activity in neural networks that will be accessible to a wide audience.

New recording methods allow researchers to probe the structure of neural activity with unprecedented scope and detail. As a result there is an explosion of interest in understanding the patterns of activity that emerge in entire neuronal populations and relating these patterns to the function of the nervous system. However, the overwhelming range of different sensory inputs that these populations receive -- and the vast range of different responses that these inputs evoke -- make it impossible to achieve this goal based on empirical observations alone. This challenge is compounded due to the nonlinearity of neuronal network dynamics, which makes it difficult to predict patterns of activity by extrapolation from observations of simpler systems. Predictive mathematical modeling and a deeper understanding of the dynamics of neuronal circuits is therefore required. With previous NSF support, the investigators developed numerical and analytic tools at the interface of statistics, stochastic analysis and nonlinear dynamics, to understand the genesis and impact of correlations in simple, but fundamental microcircuits. They build on these results by extending the underlying mathematical theory to more complex and realistic networks. Using this approach, the team of researchers examines how collective activity is controlled by network architecture, cell dynamics, and stimulus drive in a set of neural networks that typify structures across the nervous system.

Answering these questions will open the door to contemporary biological applications and will meet key theoretical challenges posed by recent technological developments in experimental neuroscience. The key innovation lies in the understanding the collective dynamics of large neural networks that cannot be decomposed into their isolated parts. Through continued interactions with a broad set of experimental collaborators, these ideas are introduced and tested by a broad community of neuroscientists. In the longer term, results on coding in the presence of collective network dynamics will impact the design of neural prosthetics, which code sensory signals via cortical, retinal, and thalamic implants.

A clear and important signature of neural response is the large degree of variability from trial-to-trial in sensory and motor tasks. Neural variability is malleable depending upon task specifics, cognitive state, and sensory input; however little is known about the mechanisms that mediate this variability. Using techniques from non-equilibrium statistical mechanics and nonlinear systems theory this project will build a coherent theory of the mechanics of neural variability. Recent experiments across cortex show that the stochastic dynamics of spontaneous neural activity is very rich, beyond that observed during evoked or task driven responses. This research will show how clustered neural architectures can replicate this finding. This research will develop key insights from simplified Markov chain models of cortical assembly dynamics, which will allow a more formal approach to our previous simulation based studies. Uncovering the core mechanics of neural variability is a critical step in giving a foundation for a theory of neural computation.

Modern computers minimize noisy fluctuations in transistors and semiconductors in order to improve performance reliability. In stark contrast, brain dynamics show a sizable trial-to-trial variability of neural responses, making it clear that the nervous system works under different principles than silicon machines. This research will use contemporary techniques from statistical mechanics and nonlinear system theory to give a theoretical foundation to the mechanics of neural variability. Specifically, our theory will expose how the underlying circuitry of the brain is involved in producing and controlling neural variability. This research will guide future experiments that aim to better characterize neural circuits, placing any data in the context of a core functional feature of the nervous system. Furthermore, our research will give critical insights concerning many neurodegenerative diseases where a common neural signature is an excess of variability.

Our brains are constantly changing. Experiences and memories leave their imprints on connections between neurons. Understanding this process is fundamental to understanding how the brain works. While this question has been of central importance to neuroscience for decades, at this moment researchers are well positioned to make significant progress -- new recording devices and imaging techniques are revealing the activity and changes within the networks of the brain at unprecedented scale and resolution. Sound mathematical models are essential to keep up with the mounting avalanche of data. The goal of this project is to develop mathematical tools to assist with improving understanding how networks of neurons are shaped by experiences. Developing this theory is crucial for understanding learning, as well as associated disorders. The project will focus on how learning improves the brain's ability to make decisions and store memories. Graduate students and postdocs joining this project will be part of an established, interdisciplinary mathematics research community. Trainees will gain a wide perspective of mathematical neuroscience through integrated research at three institutions, including extensive visits among them.

This research project builds on earlier results of this team to address a central challenge in the mathematical analysis of biophysically realistic neuronal networks: How brain activity changes brain structure over time. Understanding neural computation demands a description of how network dynamics co-evolves with network architecture. The research team will address this challenge by answering specific questions about the interplay between spatiotemporal patterns of neural activity, the attendant changes in network architectures, and the resulting neural computations. This project focuses on two main questions. First, what mathematical techniques can describe the co-evolution of network dynamics and network connectivity toward stable assemblies of neurons? To address this question this project will build a theory describing how global network structure evolves under the dynamics of biophysically realistic plasticity rules that operate on the scale of individual spikes and synapses. Analysis of these models requires novel multiscale and averaging methods. The resulting equations allow analysis of the stability of network architectures and their dependence on stimulus drive. With these results, the second question can be addressed: How does network plasticity create spatiotemporal dynamics that support the basic building blocks of neural computation? Models to understand how plasticity forms networks whose dynamics underlie specific operations on incoming stimuli will be developed to address this question. The mechanism by which long-term plasticity can reshape the connectivity of a network to encode a precise temporal sequence of events will also be investigated.

?Sensory cortex decomposes complex inputs into feature-based components, and distributes their representation over populations of neurons. In special cases this distribution is very clear--for instance the visual and auditory system respectively map retinal image and acoustic frequency along a spatial dimension within cortex. In general, however, rich sensory scenes are a mixture of features, and it remains unclear how the cortex mingles and segregates aspects of a complex sensory representation across neural populations. Olfactory stimuli are extraordinarily complex, with distinct odors comprised from a mixture of compounds. The circuitry in olfactory cortex is equally intricate, with populations of neurons coupling to one another with seemingly random rules, and receiving similarly random projections from lower centers. The combination of these two facts obfuscates the organization of odor representation. Our proposal leverages advances in experimental circuit identification and manipulation, as well as theoretical frameworks for large-scale cortical networks, to establish principles for the distribution of odor identity and concentration coding across olfactory cortex. Specifically, we aim to establish the following links between olfactory circuitry and odor coding: 1 )There exists a graded distribution of specific inhibitory sub-circuits along the rostral-caudal axis of the olfactory cortex. 2) The rostral-caudal distribution of inhibition interacts with Hebbian plasticity mechanisms so as to shape the odor selectivity of cells along the rostral-caudal axis. These advances will provide much needed insights into how cortical structures represent and process distinct aspects of an odor scene.

7. PROJECT SUMMARY Background. Electro- and magneto-encephalographic (EEG/MEG) responses to a stimulus are systematically attenuated? by up to 80%? if the same stimulus was presented less than 8-12 seconds ago. This dynamic modulation of response amplitude to identical stimuli is one of the most striking and fundamental properties of the EEG/MEG signal. The proposed work will test the hypotheses (1) that the attenuation of EEG/MEG amplitude to repeated identical stimuli is caused by short-term synaptic depression at cortical synapses and (2) that the manifestation of synaptic depression at the micro- and meso-scopic level critically depends on local circuit and network architecture leading to a complex but systematic relationship between macroscopic modulation of EEG/MEG responses and several micro- and mesoscopic measures of neural function.