Synchronous oscillations in the central nervous system represent coordinated neural activity in networks that involve extensive feedback interactions whose role is difficult to analyze. In contrast, it is experimentally feasible to measure the dynamic responses of neurons and synapses to obtain feed-forward relationships that describe how specific output variables, such as synaptic strength or dynamics, depend on input parameters such as network frequency. We propose to develop a theoretical framework in which such feed-forward relationships, as measured in a central pattern generator (CPG) oscillatory network, are combined to build recursive feedback maps-functions that describe how the variables of the oscillatory network in one cycle can be determined from those in the previous cycles. The crustacean pyloric networkis a well-studied CPG with known synaptic connectivity and provides an excellent system to develop such a framework. To characterize the dynamics of the pyloric neurons and synapses we focus on the following three categories of experiments: 1. We have previously explored the role of short-term synaptic dynamics in shaping the pyloric network output and found that pyloric pacemaker neurons and synapses have preferred (resonance) frequencies at which they respond maximally. To explore the role of synaptic and membrane resonance, we will examine the following hypotheses: A. The membrane resonance frequency of pyloric neurons can bias the network frequency through gap-junction or chemical synaptic coupling. B. Synaptic resonance increases network stability. C. Membrane and synaptic resonance are subject to neuromodulation which can change their roles in network function. D. Modulation of membrane resonance of pyloric pacemaker neurons by proctolin reduces variability of network frequency. 2. We will measure how the peak phases of pyloric synapses and the burst onset and termination phases of synaptically-isolated neurons depend on input frequency and the neuronal oscillation waveform shape and amplitude. 3. We will measure the phase response curves of the pacemaker neurons in response to synaptic inputs with distinct peak phases in control conditions and in the presence of the modulatory peptide proctolin. The hypothesis that the response properties of a bursting neuron changes when the neuron is synaptically embedded in a network will be examined. The feed-forward relationships characterized in these experiments will be described using biophysical computational models and their function in network activity will be examined using the dynamic clamp technique. From these feed- forward relationships, we will build progressively more accurate feedback maps which will be mathematically analyzed. Stable equilibrium points of such maps correspond to stable rhythmic activity and can therefore be used to determine parameters that are important for the existence and stability of the pyloric network oscillations. Because factors that change the properties of neurons and synapses, such as extrinsic neuromodulation, alter the feed-forward relationships, their effect on network oscillations can be determined by analyzing the changes in the recursive feedback maps.

Public Health Relevance

Understanding the structure and function of neuronal circuits is essential for developing treatments for mental disorders. This proposal focuses on developing experimental measurements in the context of a novel mathematical framework to understand how synaptic and neuronal dynamics contribute to circuit function in oscillatory networks in the highly accessible crustacean pyloric network. The methods and characterizations developed in this proposal can be generalized to more complex networks of the human brain to describe the emergence of biological oscillations and their disorders as observed in injury or pathological conditions resulting from demyelinating diseases, disorders of the striatum such as Parkinson's disease, schizophrenia and autism spectrum disorders.

National Institute of Health (NIH)
National Institute of Mental Health (NIMH)
Research Project (R01)
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Special Emphasis Panel (ZRG1-IFCN-H (02))
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Glanzman, Dennis L
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Rutgers University
Biostatistics & Other Math Sci
Schools of Arts and Sciences
United States
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Mouser, Christina; Bose, Amitabha; Nadim, Farzan (2016) The role of electrical coupling in generating and modulating oscillations in a neuronal network. Math Biosci 278:11-21
Kintos, Nickolas; Nusbaum, Michael P; Nadim, Farzan (2016) Convergent neuromodulation onto a network neuron can have divergent effects at the network level. J Comput Neurosci 40:113-35
Daur, Nelly; Nadim, Farzan; Bucher, Dirk (2016) The complexity of small circuits: the stomatogastric nervous system. Curr Opin Neurobiol 41:1-7
Nadim, Farzan; Bucher, Dirk (2014) Neuromodulation of neurons and synapses. Curr Opin Neurobiol 29:48-56
Kintos, Nickolas; Nadim, Farzan (2014) A modeling exploration of how synaptic feedback to descending projection neurons shapes the activity of an oscillatory network. SIAM J Appl Dyn Syst 13:1239-1269
Akcay, Zeynep; Bose, Amitabha; Nadim, Farzan (2014) Effects of synaptic plasticity on phase and period locking in a network of two oscillatory neurons. J Math Neurosci 4:8
Bose, Amitabha; Golowasch, Jorge; Guan, Yinzheng et al. (2014) The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations. J Comput Neurosci 37:229-42
Tseng, Hua-an; Martinez, Diana; Nadim, Farzan (2014) The frequency preference of neurons and synapses in a recurrent oscillatory network. J Neurosci 34:12933-45
Rotstein, Horacio G; Nadim, Farzan (2014) Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents. J Comput Neurosci 37:9-28
Oh, Myongkeun; Zhao, Shunbing; Matveev, Victor et al. (2012) Neuromodulatory changes in short-term synaptic dynamics may be mediated by two distinct mechanisms of presynaptic calcium entry. J Comput Neurosci 33:573-85

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