Nancy Kopell - US grants

8901913 Kopell This project is to study a variety of questions relating to central pattern generators (C.P.G.'s), which are neural networks that govern the stereotypic aspects of rhymthmic motor activity. These networks often involve oscillating subnetworks or cells interacting with other oscillators or non-oscillating neurons. One of the most studied C.P.G.'s is a network that is roughly configured as a chain of oscillators. One goal of the mathematics is to intuit and test conjectures about general kinds of constraints on the connectivity, in order that the network be able to function appropriately. The current effort builds on former results and focuses on three areas: (1) the role of long-range coupling in the network, (2) the construction of networks not composed of modular oscillatory subpieces, but behaving like chains of discrete oscillators, (3) the interaction of the neural activity of the C.P.G. with the mechanical activity that it directs. In addition, work is proposed on issues arising from small invertebrate network C.P.G.'s. The focus of that work is to relate properties of the cells to emergent properties of the network. All work is to be done in coordination with experimentalists. Finally, some purely mathematical topics are proposed.

Oscillatory neural networks and oscillatory neurons are common in the nervous system. Yet the function of neural networks that contain OsCillatory elements is largely unexplored. The proposed work aims to develop a body of technique relevant to addressing this relationship, and to use this technique to further the understanding of some particular neural networks. The work will focus on one vertebrate and one invertebrate neural network, both central pattern generators (CPGS) engaged in producing rhythmic motor output. In each case, the work will be collaborative with neurophysiologists whose data will constrain the modelling activities. The vertebrate CPG to be studied is that for undulatory locomotion; the main experimental animal is the lamprey. This work continues a collaborative effort to formulate and investigate a general and flexible mathematical framework within which conclusions may be drawn from experimental data on the lamprey about how the network functions. Work in the immediate future will focus on the properties of long range coupling among the ii local oscillatory elements, the implications of the design of local networks for the global emergent behavior, and the interaction between the neural behavior and the mechanical activity that it regulates. Relevant experiments will be designed and carried out. The invertebrate CPG is the crustacean stomatogastric ganglion (STG). This work is part of a larger project involving modelling and experiments. Our part of the project is to develop mathematics to help address such questions as: (i) How can the behavior of the network be explained on the basis of the properties of the component neurons? (ii) How do pacemaker and emergent modes of oscillation, that are both known to exist in the STG, interact and cooperate to produce stable and flexible system behavior?

The investigator develops mathematical methods for analyzing oscillatory networks of neurons. Such networks are common in the central nervous system, but so far the relationship between structure and function in them is largely unexplored. Some of the specific projects are tightly connected to the analysis of particular neurophysiological networks, such as the vertebrate central pattern generator for undulatory locomotion. This work is undertaken in collaboration with a group of neurophysiologists. Others are designed to develop new methods to analyze such networks. In particular, neurons and networks of them operate on many different time scales, and new mathematical techniques are needed to understand the range of behaviors that can result as a consequence. The mathematics is used to help determine which features in the neurons or their connectivity is responsible for the emergent behavior seen in physiological preparations or in computer simulations of them. Mathematical techniques that have been useful for earlier stages of this work include reduction procedures that produce simpler equations having similar behavior. New techniques to be developed include geometric methods for the analysis of equations with many time scales. Some of the project topics concern the development of such techniques independent of biological questions. Central pattern generators are neural networks -- clusters of neurons connected together -- that are thought to govern rhythmic motor activity such as walking, running, swimming, and breathing. These generators are examples of oscillatory networks of neurons. The project aims to develop a better understanding of the relations between the structure of oscillatory networks and the behaviors of the networks. Such understanding is fundamental for a variety of neurophysiological questions.

Kopell 9706694 The investigator and her colleagues study the dynamics of networks of neurons, especially networks whose output is rhythmic. The research uses methods of dynamical systems to understand how properties at the cellular level (intrinsic membrane dynamics) and the interconnections among the cells (synaptic properties) affect the network behavior. The research focuses on two kinds of problems. The first concerns the mechanisms by which networks synchronize or partially synchronize. These problems mainly concern cortical networks in which there are large numbers of similar cells. The other class, motivated mainly by smaller invertebrate networks, is concerned with the determination and regulation of network frequency and relative phases among cells in the network. In both classes of problems, the work is motivated by specific networks of neurons, but the techniques are broad enough to allow generalization of the results beyond the motivating examples. The dynamical systems methods to be used and developed exploit the many different times scales associated with the intrinsic and synaptic dynamical processes of the cells. One goal is to understand how network behavior is modulated by changing parameters that alter which subset of dynamical processes is most important in producing the network output. Networks of neurons producing rhythmic output are found in neural systems governing motor control, sensory processing, and in both sleeping and awake states. Rhythmic activity in the nervous system is also seen in pathological states, such as epilepsy and Parkinson's disease. Though there is much detailed information about the physiology of participating cells, it is not understood how networks that make use of dynamically complicated components are constructed to carry out their appropriate tasks. This research aims to identify mechanisms by which coherence, frequency and phase relationships of the rhythmic network output are regulated. Such identification can potentially allow scientists a deeper understanding of how the nervous sytem uses rhythms to produce appropriate behavior, as well as techniques for removing rhythmic activity that produces pathological states, including tremor.

The investigator and her colleagues collaborate in a group
project at the Center for BioDynamics (CBD) to provide
interdisciplinary education and training for graduate students
and postdoctoral-level investigators in the context of a vigorous
interdisciplinary research program that focuses on areas of
mutual interest in mathematics (especially dynamical systems),
biology, and engineering. Disciplines include mathematics,
biomedical engineering, aerospace/mechanical engineering,
biology, psychology, and physics. Training extends beyond the
usual classroom activities by engaging participants in a variety
of research projects as well. One of the major topics is dynamics
of the nervous system. The projects, which involve experiments,
modeling, and analysis, all deal with the variety of rhythms in
the nervous system and the potential functions of these rhythms
in key cognitive states and processes such as attention,
awareness, learning, and recall. A second major topic is
dynamics of gene expression. Progress in genomic research is
leading to maps of the building blocks of biology and fueling the
study of gene regulation, where proteins often regulate their own
production or that of other proteins in a complex web of
interactions. CBD projects focus on using techniques from
nonlinear dynamics, statistical physics, control theory, and
molecular biology to model, design, and construct synthetic gene
regulatory networks, and to probe naturally occurring gene
regulatory networks. The third major topic is the dynamics of
patterns and waves. Training activities include two weekly
working seminars, extra journal clubs and reading groups,
seminars to educate the CBD members in the research going on
within the Center, and a CBD-initiated team-taught course.
The Center for BioDynamics (CBD) helps to advance
understanding of difficult interdisciplinary problems at the
intersection of mathematics, biology, and engineering, and it
trains mathematicians, scientists, and engineers for the 21st
century workforce. It does this by combining traditional
classroom education with significant engagement of students and
postdocs in interdisciplinary teams working on current problems.
The disciplines involved are mathematics, biomedical engineering,
aerospace/mechanical engineering, biology, psychology, and
physics. One of the major topics is dynamics of the nervous
system. The projects in this topic seek to shed light on the
origin of the electrical activity in the brain, and how the brain
uses this activity to process sensory information, to think, and
to regulate movement. A second major topic is dynamics of gene
expression. The web of interactions among the proteins that are
produced by genes is complex; the projects associated with this
topic involve the design and construction of artificial gene
regulatory networks, and techniques to better understand
naturally occurring gene regulatory networks. The third major
topic is the dynamics of patterns and waves, occuring in a
variety of applications. Training activities include two weekly
working seminars, regular sessions to read scientific journals,
seminars to educate the CBD members in the research going on
within the Center, and a CBD-initiated team-taught course. The
project is supported by the Computational Mathematics, Applied
Mathematics, Computational Neuroscience, and Biological Databases
and Informatics programs and by the MPS Office of
Multidisciplinary Activities.

DESCRIPTION (provided by applicant): Rhythms of the nervous system have been linked to important behavioral and cognitive states, including attention, working memory, associative memory, bottom-up feature binding, object recognition, sensory motor integration, perception and language processing. Pathologies in the rhythms have been linked to schizophrenia and Alzheimer's disease. Although these rhythms have been detected both in vitro and in vivo, how they participate in cognition is still not understood. The general aim of this proposal is to make use of biophysical information about cells and synapses in modeling studies to understand the origin and mechanisms of coherence of the various rhythms displayed in nervous system. Some of this information exists from previous experiments. Other data will be gathered in experiments proposed here. The proposal focuses on three important rhythms: gamma (30-80 Hz), beta (12-30 Hz) and theta (4-11 Hz). A major goal of this work is to understand how the mechanisms that produce the rhythms influence the way the nervous system processes structured input. There are many experimental paradigms that produce different versions of rhythms with the same frequency range. These are analogues of different in vivo situations, and can have different reactions to pharmacological perturbations. In different versions of the same frequency rhythm, there are different synaptic conductances that are critical and there may be different classes of interneurons participating. The modeling aims to probe the roles of the different intrinsic and synaptic currents in producing the individual rhythms and the interactions among them, including nesting rhythms and the transitions among them that are associated with changes of behavioral state. Experiments, done in tandem, aim to reveal more details of the electrophysiological and pharmacological properties of the classes of interneurons, and roles of electrical synapses in producing rhythms. There will also be experiments aimed at teasing out different rhythms in different layers of the neocortex. Other experimental paradigms will probe effects of sensory stimuli, the importance of synaptic plasticity in the transformation among rhythms, and the conditions under which nesting of gamma and theta occur. We will also study, both experimentally and via modeling, separated networks that produce a coherent gamma rhythm, and networks distributed over space.

The investigator studies systems with multiple interacting
components that together create rhythms. The systems come from
neural, chemical, and gene regulatory contexts. There are two
main themes. The first is reduction of dimensions, investigating
the circumstances under which large-dimensional models behave
like much lower-dimensional differential equations or maps. Some
of that work uses geometric singular perturbation theory to
investigate how systems with multiple degrees of freedom
"condense" to essentially lower-dimensional systems, at least
locally in phase space. Another set of issues related to
reduction of dimension concerns fast partial synchronization.
The second theme concerns how interaction of many components in a
system can lead to the suppression of activity in some of the
components. Two examples of this to be studied come from a
chemical pattern formation and neural systems, each with some
type of global inhibitory feedback.
Systems with many separate but interacting components arise
in a large variety of applications, including biotechnology,
chemical engineering, and neurobiology. In general, such systems
have a large number of degrees of freedom, and are usually
investigated by numerical simulation. However, simulations alone
do not provide a deep understanding of why the systems behave the
way they do, or how they can be manipulated. Reductions of
equations to smaller systems can be very useful. But without a
principled way to do the reductions, one does not know how much
of the behavior of the large system is lost. This project
concerns methods to find such principled reductions, using
mathematical tools that enable one to investigate circumstances
under which parts of the dynamics behave like that of systems
with a much smaller number of degrees of freedom. Other tools to
be used allow one to understand how only some subset of the
components can be involved at a given time, even though all
components are coupled. The methods are applied to problems from
neural, chemical and gene regulation systems. The project also
provides interdisciplinary training opportunities for students
and postdocs.

This project will advance the creation and support of a community of scholars, from undergraduate to faculty, working at the interfaces among dynamical systems and biological applications. The three main areas of focus are: 1. Analysis of systems with multiple length and time scales, including applications to pattern formation; 2. Mathematical neuroscience, including analytical methods for working with small networks and reduction of dimension techniques; 3. Gene regulatory networks, including the development of RNA switches, transcriptional bursting and programmable cells. These areas have major applications to issues concerning health and medicine. The project will build on the previous research and training experience of the Center for BioDynamics, co-directed by the Principal Investigator and one of the other senior faculty members. Trainees will be pre- and post-doctoral students who will take part in a wide variety of formal and informal activities, including special seminars, working groups, mini-symposia, laboratory work, journal clubs and social events, which will enable them to acquire the multiple scientific cultures needed to work in a trans-disciplinary manner. The pre-doctoral students will be from the departments of Mathematics or Biomedical Engineering; the postdoctoral associates will be drawn from a wide range of backgrounds, with a focus on applied math. In addition to their research activities, trainees will obtain experience teaching at different levels. Math department faculty and trainees will be involved in the construction of new interdisciplinary curricula for undergraduates in other departments, including Biology; the faculty will mentor the trainees in teaching the new curricula.

The nervous system produces electrical activity in all cognitive states, and this activity generally displays significant power at any given time in multiple frequency bands. This project focuses on the mathematical issues that have been raised by previous large-scale simulations, and seeks to get a deeper understanding of how the qualitative properties of intrinsic and ionic currents in single cells shape the complex behaviour that has been seen in a variety of simulations of large and small networks. The work focuses on two specific situations which present many of the general issues. The first is the interaction of the gamma (40-90 Hz) and theta (4-12 Hz) rhythms in the hippocampus. As shown in previous numerical and experimental work, the gamma and theta rhythms appear to be produced in vitro by different sub-networks of hippocampal neurons, with some components in common; simulations have shown that changes in parameters can switch control of the common elements and change the power in the different frequency bands. The project considers the global bifurcations involved in switches of control. The second situation concerns changes of brain rhythms in the presence of the anesthetic propofol which, at the biophysical level, acts mainly by increasing the decay time and amplitude of GABA_A mediated inhibition. A central question of the previous modeling work is the origin of the so-call "beta buzz", in which a low dose of propofol excites, rather than sedates, the patient, with an increase in the power in the beta frequency bands (13-30 Hz) and a decrease in lower and higher frequency bands. Simulations have shown this un-intuitive behaviour in model networks having multiple components, notably by the creation of "clustering" of inhibitory cells into subgroups firing in antiphase, transforming low frequencies into higher ones. Kopell mentors many graduate students and postdoctoral fellows; this project ties mathematical analysis to other work focusing on function, and thus allows trainees to see how mathematics can be used to bridge from biophysics to function.

The nervous system produces electrical activity in all cognitive states, and this activity generally displays significant power at any given time in multiple frequency bands. This project focuses on the mathematical issues that have been raised by previous large-scale simulations, and seeks to get a deeper understanding of how the qualitative properties of intrinsic and ionic currents in single cells shape the complex behaviour that has been seen in a variety of simulations of large and small networks. The work addresses the general issues of how the brain produces its multiple frequencies, and how changes in biophysics can change the mixture of dynamic components. In the first sub-project, this is linked with the central question of how networks react to inputs with spatial and temporal structure reflecting the coding of information. In the second, the work helps to bridge the knowledge of biophysical effects of an anesthetic to its functional properties (inducing loss of consciousness) by tying the biophysical changes to changes in dynamics known to be related to cognitive state. The analytical tools proposed have been used in much simpler contexts. The work will require the development of extensions to allow application to larger and more complex networks. The extensions should be applicable to a wide range of neural applications. Kopell is co-Director of the Center for BioDynamics and the Program in Mathematical and Computational Neuroscience at Boston University. In this context, she works with and mentors a large number of graduate students and postdocs, including many women. This project ties mathematical analysis to other work focusing on function, and thus allows these and other trainees to see how mathematics can be used to bridge from biophysics to function.

This project focuses on the functional implications of low-frequency rhythms in the basal ganglia and neocortex. The collaborative effort involves four groups: Kopell, (Boston University), Moore (Massachusetts Institute of Technology), Graybiel (Massachusetts Institute of Technology) and Boyden (Massachusetts Institute of Technology). The project is the first collaborative research effort of the newly formed Cognitive Rhythms Collaborative (CRC), a group of Boston Area faculty members from Boston University, Massachusetts Institute of Technology, Massachusetts General Hospital Martinos Center for Biomedical Imaging, Brandeis University and Tufts University. The aims of the CRC, which fosters research and training, are to map the spatio-temporal structure of brain dynamics and connect these dynamics to brain function. This is the first project to try to understand from basic electrophysiology the growing literature suggesting that the low frequency brain rhythms are critical for both attention and learning, and that interactions among brain structures such as the basal ganglia and neocortex are central for such functions. The project makes use of the electrophysiology skills of the Graybiel lab, which is focused on the dynamics of the basal ganglia, and those of the Moore lab, focused on the neocortex, to understand the flow of information between the cortex and the basal ganglia during learning and attention. This collaboration is enriched by new molecular biology technology developed by the Boyden group. This technology, in which cells can be activated and inactivated by light, provides powerful new techniques for figuring out circuits by looking at effects of perturbations, even in behaving animals. The experimental work is guided by modeling ideas from the Kopell and Moore labs, and the output of the modeling can be tested almost immediately by the labs for quick feedback and changes. This CRC project exemplifies a new and transformational way of doing science, bridging the boundaries of disciplines and institutes to facilitate cutting edge research at the forefront of interdisciplinary endeavors.

DESCRIPTION (provided by applicant): This project concerns the physiological mechanisms of brain oscillations in the neocortex, a structure vital for perception, thought and memory. Brain oscillations are believed to be important for sensory processing, cognitive states such as attention, and for motor planning. Pathological alterations in brain oscillations have been shown to correlate with the existence of, and progression of, a variety of neuro-psychiatric conditions, including epilepsy, dementing disorders, and schizophrenia. Recent in vivo and in vitro data have demonstrated that a given cortical region can express, simultaneously, two different oscillations, produced (in the in vitro case) in different laminae. There are also numerous examples, in vivo, of oscillations of different frequency that are nested. Though considerable progress has been made in understanding the mechanisms underlying the generation of individual cortical rhythms, much less is known about multiple interacting neural rhythms seen in vivo and in vitro. The broad aims of this project are to examine, in further detail, the mechanisms of high-frequency brain oscillations, and to use that information as a platform for the study of spatiotemporal interactions of concurrently generated rhythms at the same, or at different, frequencies. We seek to understand how multiple oscillations may be co-expressed in single or interconnected networks, and how they may interact to facilitate cortical information processing. The specific aims of the project include the analysis of selected high-frequency rhythms (gamma (30-80 Hz) and synapse-dependent beta2 (20-80 Hz) rhythms generated in deep layers, very fast (>80 Hz) oscillations);the factors that determine when deep layers express gamma or beta2;the interactions of multiple rhythms within a single cortical column;the dynamics of multiple columns connected in an anatomically realistic manner. Techniques include both detailed and reduced network modeling. Better understanding of the cellular mechanisms of brain oscillations, and how oscillations become grouped together, could provide information as to whether "oscillation repair" is a reasonable clinical goal, in the sense that clinical interventions that normalize brain oscillations might also improve clinical symptoms. It may also help in the eventual use of brain oscillation signals as inputs to brain-machine-interface devices. PUBLIC HEALTH RELEVANCE This project concerns the physiological mechanisms of high frequency brain oscillations in the neocortex, a structure vital for perception, thought, and memory. Pathological alterations in these brain oscillations have been shown to correlate with the existence of, and progression of, a variety of neuropsychiatric conditions, including epilepsy, dementing disorders, and schizophrenia. Better understanding of the cellular mechanisms of brain oscillations, and how oscillations become grouped together, could provide information as to whether "oscillation repair" is a reasonable clinical goal, in the sense that clinical interventions that normalize brain oscillations might also improve clinical symptoms.

DESCRIPTION (provided by applicant): Gamma frequency oscillations (30-90 Hz) are found in many parts of the nervous system, including the hippocampus, neocortex, entorhinal cortex and amygdala. They are believed to be important for a range of functions, including attention, early sensory processing, short term memory, motor activity. Mental illnesses, notably schizophrenia, are associated with pathologies in this rhythm, and many people are now studying these pathologies for clues to the pathophysiology of the diseases. At a simple level of description, gamma oscillations are thought to come about as interactions of parvalbumin positive (PV+) fast-spiking (FS) interneurons and pyramidal cells. However, it is known that other cell types, especially interneurons, participate in gamma rhythms and/or may modulate power and coherence of those rhythms. To understand the functional importance of these rhythms, it is necessary to better understand mechanisms that create and modulate them. Here we propose to use, for the first time, the combination of mathematical modeling with application of a set of emerging techniques involving molecular biology, optics, and electrophysiology to study the cell-type specific and circuitry properties of networks that produce gamma oscillations in the cortex. We will use in vitro models of the primary auditory cortex, with gamma oscillations induced using the glutamatergic agonist kainate or the cholinergic agonist carbachol. Specific classes of cells will be activated or suppressed by brief or longer periods of light. The work will focus on pyramidal cells, PV+ cells, cholecystokinin-expressing (CCK+) cells and somatostatin-containing (SOM+) interneurons. Minimal models will be constructed of these cells types and networks containing all of them. The model networks will be used to understand how the CCK+ and SOM+ interneurons interact with the PV+ cells to alter the gamma rhythms, in connection with experimental manipulations of the activity of different cell types. The experiments and models will also be used to understand how the CCK+ and SOM+ cells may affect the creation of cells assemblies. Broader Impacts: This work is part of a broader set of research by these labs on the importance of dynamics in cognitive function. The investigator is head of the Cognitive Rhythms Collaborative in the Boston area, a group of about 20 senior scientists, whose aim is to create and support new collaborations, including those making use of basic science and modeling in the study of disease, including Epilepsy, Parkinson's Disease, Autism and Schizophrenia. The work done in this project will provide new science that will interact with the work of many others in that group. The experimental work provides, for the first time, a combination of molecular biology, optics, and electrophysiology to study the cell-type specific and circuitry properties of networks; these techniques, pioneered by a member of this group, can then be used in many other contexts, beyond this group. The techniques and results will help provide information about the pathophysiology of mental illnesses; this has the potential of controlling such diseases by correcting the oscillapathy (defects in brain dynamics) associated with the symptoms. Finally, the specific project will also help train two graduate students and a postdoctoral fellow.

This grant supports the Collaborative Rhythms Collaborative (CRC), a group of scientists in the Boston area who have begun to work together to advance our understanding of the brain dynamics underlying cognitive functions such as attention, sensation, motor planning, and memory. There is a growing consensus that dynamics are central to understanding how the brain works, but major gaps exist in what we know and in how we seek to understand more. The CRC has focused on the dynamical regime most strongly associated with cognition, rhythmic activity in the frequency range 1 - 200 Hz. Its central aims are to characterize the physiological origins and functions of such rhythms and to understand how pathologies in rhythmic dynamics are related to symptoms and mechanisms of neurological disease. Mathematical modeling, cutting-edge statistical techniques, and their implementation as computer algorithms will be critical to carrying out its scientific program. The grant will support the CRC, concentrating on the application of the mathematical sciences to the investigation of brain dynamics and the potential for new mathematical, statistical and computational techniques driven by challenging scientific problems. This will include support of a technology core that will create new hardware/software platforms to support such techniques. The CRC will also provide mentoring and teaching to a large community of students and post-doctoral fellows.

The Cognitive Rhythms Collaborative, involving multiple institutions in the Boston area, offers a unique chance to develop a network of researchers from the mathematical, biological, and cognitive sciences to explore fascinating questions in the area of neuroscience. This is a different mechanism of interaction than is traditionally seen and has the potential to transform the way such interdisciplinary problems are addressed. The CRC seeks to provide new ways of doing science by fostering broader and deeper collaboration in addressing scientific questions. This work will involve tight collaborations among scientists with a multitude of backgrounds, and will emphasize the role of mathematics in the investigation of neuroscience questions. The CRC will also train a cohort of postdoctoral fellows in a way that will lead to a deep understanding of the intellectual context of their work. The technology core of the project will produce both hardware and software that will be available within and beyond the CRC, and enable computations that are now almost impossible.

Forced networks of oscillating neurons are ubiquitous in the nervous system. Although forced unitary oscillators have been heavily studied, there are very few studies of the effects of periodic forcing on networks of oscillators with multiple internal degrees of freedom. Understanding such systems is an essential step in understanding how the brain makes use of its rhythmic dynamics to communicate signals among regions. The networks in this project have an almost universal property of networks of neurons: there is exponentially decaying inhibition that feeds back to the excitatory cells of the network. In these projects, the decaying nature of the inhibition is important for the emergence of lower-dimensional dynamics and the ability to produce and analyze simplified models of network phenomena. The initial three subprojects concern noise, multiple periodic inputs, and intrinsic currents providing extra timescales that interact with periodic forcing. The work will relate the properties of network interaction, such as the decaying inhibition, to geometric ideas of invariant manifold theory. The aim is to produce a level of mathematical clarity that is not generally a part of initial modeling work, and to expand the set of tools and concepts available for further study of forced networks. The project focuses on networks producing gamma (30-80 Hz) oscillations and beta (12-30 Hz) oscillations, with physiological descriptions of the neurons appropriate to those rhythms.

The dynamics of the nervous system are central to cognitive function, but how the brain makes use of its dynamics is barely beginning to be understood. Rhythms of the nervous system have long been known to be highly associated with cognitive processes including sensory coding, attention, learning, memory, and motor planning. The study of such rhythms, and their use in brain communication, is an excellent bridge between physiology and function. This project deals with the response of networks of neurons to periodic and other input, as would be seen from signals arriving from other parts of the brain. The purpose of the project is to understand how brain networks process their temporally and spatially coded inputs. This work is being done in the context of a broad initiative to study the origin and significance of brain rhythms. Kopell is the founder and current head of the Cognitive Rhythms Collaborative, a group of over two dozen Boston-based senior investigators interested in the physiological and dynamical mechanisms of neural activity, their importance in cognition, and their pathology in neurological diseases including schizophrenia, Parkinson's disease and epilepsy, as well as their changes in anesthesia; it includes experimentalists working in vivo and in vitro, mathematicians, statisticians and medical personnel, who are already incorporating ideas from the mathematical research into clinical practice.

The development of quantitative theories of learning, memory, and prediction is fundamental to understanding human cognitive processing. This workshop, to take place in Arlington VA, May 8-9, 2014, tackles a key scientific need: to integrate modern complex systems and network approaches with understanding cognitive function. Predictive models of higher order cognitive processes could inform the development of neuroprosthetics, facilitate advances in brain-computer interfaces, and assist in the construction of intervention protocols for cognitive deficits that accompany neurological disorders and psychiatric disease.


Understanding how the human brain works has emerged as a major international focus of research in the coming decade, identified as such in President Obama's State of the Union Address in February 2013 and further developed in President Obama's BRAIN initiative announced on April 2, 2013. This workshop will bring together systems neuroscientists, cognitive scientists, applied mathematicians, and theoretical physicists. The aim is to identify a set of achievable goals that integrate dynamic, quantitative theories of cognition with neuroscientific and theoretical avenues of research.

It is now well accepted that cognitive functions are supported by activity dispersed throughout the brain, and that signals are passed among participating regions of the brain. Indeed, there is an active direction of study, known as connectomics, that seeks to find such connections on multiple spatial scales. It is not sufficient, however, to find what regions are connected. Rather it is important to determine how and in what directions regions are connected. How are signals conveyed and acted upon as part of a neural computational process? To understand such neural computations, it is necessary to understand how input patterns of signals in space and time are processed at the target network. This is a huge scientific program in which mathematics and modeling can play a central role in guiding experiments. The aim of this research is to produce a body of work that is representative of the general issues that are encountered in adding input that has timing structure to networks exhibiting rhythmic structure. From such a body of examples, a goal of this project is to search for general principles about networks of neurons with external input. Such forced networks are far more complex than the well-studied phenomena of simple forced oscillators. This project will support two graduate students and will be carried out within the context of the Cognitive Rhythms Collaborative, a NSF-supported group of more than two dozen labs (mostly) in the Boston area working on brain dynamics and cognition. The CRC is designed to facilitate collaborations among its many groups, with special attention to the graduate students and postdocs of these groups.

This project is concerned with the effects of input signals with multiple time scales on target networks of neurons that also have multiple time scales. From the huge number of examples of these phenomena manifest in the nervous system, this research is focused on two of particular biological importance. The first is the interaction of gamma and theta rhythms, mainly in hippocampal networks, with inputs from other parts of the hippocampus and neocortex also carrying such temporal patterns. The second concerns a rhythm that has been experimentally and computationally investigated in a region of parietal cortex in vitro; parietal cortices are known to be hubs of connections, with inputs from many other areas. The particular rhythm in question arises as an after-effect of stimulation, and has been shown computationally to change the network response to later tonic excitation. This research will improve understanding of the effect on a network displaying this rhythm of input with more complex spectral properties, such as inputs from other brain regions. The networks involved have both excitatory and inhibitory cells, sometimes with more than one kind of inhibitory cell producing multiple time scales in the target network.

Abstract We will use detailed biophysical (Dynamical Systems) modeling to pursue two large questions critical to integrating and understanding the results of Projects 1-4. What are the physiological origins of the brain rhythms studied empirically in Projects 1-4? How do network level rhythms depend on the physiological properties of the underlying neuronal ensembles? Modeling uses differential equation descriptions of physiology at the level of single cells, synapses and networks. Data from Projects 2 and 4, along with prior models and in-vitro findings, will help to build and refine physiologically-plausible cell circuit models that generate oscillations. Models will help investigate how local brain rhythms, periodic (and aperiodic) sensory inputs and top-down signals combine in Active Sensing. We will rigorously test questions concerning the neuron populations, interconnections and cellular processes (e.g., conductances) that generate specific rhythms (e.g., alpha and delta) in multiple parts of the brain during Active Sensing tasks. Laminar activity profiles sampled concurrently from multiple cortical and thalamic areas in Projects 2 and 4 will allow us to model and constrain rhythmic dynamics at a network level, which is the a-priori level of analysis in Projects 1 and 3. In an ?iterative loop,? models will generate testable predictions at cellular, cell-circuit and and small network levels to be tested in monkeys, and at larger network levels to be tested in humans (Core A), in each case feeding back into the modeling. Our SPECIFIC AIMS are: AIM 1: Model thalamocortical interactions underlying intrinsic sampling rhythms in Active Sensing. AIM 2: Model the physiology of selective thalamocortical entrainment to rhythmic input. An ongoing R21 AIM 3: Model the large scale circuitry orchestrating distinct operational modes of Active Sensing.. CENTER SYNERGIES: This project will use thalamic and cortical data from Project 4 to model cortical and thalamic interactions in selective entrainment to ?extrinsic? rhythms, and data from Project 2 to model cortical and thalamic interactions underlying ?intrinsic? rhythmic sampling of sensory input. After the computational models have incorporated sufficient empirically-derived information, results that make testable new predictions for the physiology studies will be used to refine their analyses. They will also provide tools with which to explain the effects of thalamic projections on cortical coherences seen in the analyses of projects 1 and 3. Specific model predictions will be tested with phamacological manipulations in monkeys, and with direct brain stimulation in monkeys and in selected ECoG sstudies (Core A), and the results will refine the model.

Classical conditioning has been studied in many different animal models, and even in humans. However, the larval zebrafish with its transparent brain offers a unique opportunity to observe large scale changes in synaptic structure that accompany this form of learning. Accordingly, we have developed a novel paradigm for visualizing synaptic changes that occur during classical conditioning in larval zebrafish. Using this paradigm we have observed striking region-specific changes in the distributions of synapses that drive the rewiring of neural circuits that mediate threat responses. In this grant we will expand this paradigm by monitoring neuronal activity through imaging of genetically encoded calcium indicators throughout the pallium (the homolog of the amygdala) before, during and after classical conditioning and extinction. This will allow us to identify cells that comprise the circuits that control threat and safety and explore their connectivity using optogenetics. We will investigate how different sensory inputs can cause changes in the activity of those cells leading to synapse change, and the formation or extinction of associative memories. A crucial component of these studies will be the recording of field potentials to capture rhythmic activity throughout the pallium and high speed SPIM imaging of genetically encoded voltage indicators to record rhythms in individual cells. By understanding the precise timing of signals that impinge on individual cells we will uncover mechanisms that underlie synaptic plasticity. Our goal is to develop a theoretical model describing the neural circuits that underlie threat detection and how they can change as a result of associative memory formation and extinction.