Farzan Nadim, PhD - US grants

PI: NADIM
Abstract

Rhythmic motor patterns such as walking, swimming and digestion of food are fundamental behaviors in all living animals. These behaviors originate in electrical signals produced by complex networks of the central nervous system. The underlying mechanisms that generate and coordinate these electrical rhythmic patterns are only now beginning to be understood. We study rhythmic pattern generation in a small neuronal circuit, the pyloric network of the lobster Panulirus interruptus. This network is responsible for controlling the muscles involved in chewing and filtering of food in the lobster. This network is an ideal model system for understanding rhythmic motor activity due to its experimental accessibility and small number of neurons.
We focus on understanding how the pyloric network output is shaped by the dynamic behavior of its synapses. We record neuronal waveforms during an ongoing pyloric rhythm in vitro. We then play back these realistic waveforms into the network in
controlled conditions with the aid of a computer. The synaptic response to these waveforms are analyzed and used to build computational models. These model synapses are, in turn, interfaced with the biological network in real time and thus tested directly in an experimental setting. The goal of this work is to further our understanding of the neural basis of behavior by building realistic models that accurately reproduce the behavior.

DESCRIPTION (provided by applicant): 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.

Intellectual Merit: The enormous recent interest in biological research by physicists, computer scientists, engineers and mathematicians has been inspired in part by advances in mathematics, computing capabilities, and the realization that biological systems are often amenable to study as complex dynamical systems.

This has led to a growing interest in exploring potential applications of these new tools and ideas within the biological sciences. On the other hand, almost all disciplines in biology, including neurobiology, biophysics, ecology, and cellular and molecular biology, have seen a rising interest and need for cross-disciplinary research with mathematics.

The investigators are developing an Undergraduate Biology and Mathematics Training Program (UBMTP) to educate undergraduate students in an environment in which mathematics and biology are intimately linked at both the curricular as well as the research level. A primary goal is to teach students the separate languages of mathematicians and biologists so that these students will be able to converse with either language, and to understand both. Students who emerge from this program are able to study biological problems from an analytic and modeling point of view. They are also capable of applying mathematical techniques to biological problems and are able to translate biological questions to mathematical ones, and mathematical answers to biological ones.

Broader Impact: While the recent history of collaboration between mathematicians with experimentalists has proved fruitful, it has been so short that very few researchers have "grown up" with the idea that mathematics and biology are, or could be, intimately linked. Instead, most of the current interdisciplinary researchers began their careers working solely in either mathematics (or a related area) or biology, and only switched into the other field at the post-doctoral level or later. While bringing new and fresh ideas to the other camp, these researchers needed, and continue to need, a significant time to acquire expertise in their new interdisciplinary field. This project begins the interdisciplinary training of students at an early stage of their careers, namely at the undergraduate level.

The goal is to enhance the biological abilities of mathematicians and mathematical abilities of biologists. At a more fundamental level, the project trains students to recognize how mathematics and biology complement one another, thereby allowing them to not only formulate novel hypotheses, but also equipping them with the tools needed to test their predictions. The training program is based on the following aims:

1) Conduct targeted recruitment of students majoring in biology and mathematics.
2) Develop a directed interdisciplinary curriculum for the UBMTP.
3) Train students to conduct independent research.
4) Foster scientific discussion and interactions.

The proposed program brings together 14 investigators from the Department of Mathematical Sciences and the Federated Department of Biological Sciences, a department that includes not only NJIT faculty but Rutgers-Newark faculty as well. The faculty of both departments appear to have a long tradition of interdisciplinary and collaborative research. The large number of faculty provides broad possibilities for research projects. These include neurobiology, developmental biology and ecology. Students gain an in depth experience that spans two academic years and the intervening summer, providing outstanding continuity.

The primary goal of this project is to provide a new understanding of the neuronal properties that are critical for producing stable slow bursting oscillations and to explore the consequences of their activation when neurons expressing them are embedded in a network. Nonlinear regenerative inward currents are thought to be important in producing slow oscillations and bursting. This project uses a novel approach where the nonlinear inward current is replaced with a linear current of negative conductance. This approach exposes the multiple roles played by regenerative inward currents and simplifies the investigation of the contribution of other ionic currents to oscillatory activity. It also allows for a simpler mathematical analysis of the mechanisms that generate neuronal oscillations. This methodology is used to investigate the role of specific ionic currents in the generation and shaping of oscillations in individual neurons, to examine how synaptic interactions between neurons cooperate or compete with intrinsic properties to produce oscillations in networks of heterogeneous neurons, and to determine if the mechanisms that give rise to oscillations in isolated cells remain unchanged when the neuron is part of a network. These aims are pursued using techniques of dynamical systems and bifurcation theory in reduced mathematical models as well as simulations of detailed biophysical models, and electrophysiological experiments on bursting neurons of the crab pyloric network. These three methods are developed in parallel allowing for continual exchange of findings between the theoretical and experimental approaches.

Numerous behaviors ranging from locomotion to cognitive tasks rely on oscillatory activity generated by networks of neurons in the brain. Despite the predominance and indispensability of brain oscillations, few theoretical tools are available for understanding how such oscillations are generated or controlled. A novel approach is used that combines biological experiments and mathematical analysis to break apart the complex interactions present in network components into simple building blocks. This allows core elements that are important in the generation of oscillations to be extracted and will clarify the role of other existing components in sculpting behavior using mathematical models. The models are tested through experiments that connect real time computer-simulated neurons to small oscillatory networks in the crab central nervous systems. This project provides a framework for developing neural-based control systems with potential applications in robotics and bio-inspired computing.

DESCRIPTION (provided by applicant): The neural code is expressed as either the rate or the timing of action potentials (spikes). Yet, spike patterns can be affected by changes in the speed and precision of axonal spike propagation, by spike failures or generation of ectopic spikes in the axon. These phenomena depend on the axon morphology, passive membrane properties, and the complement and properties of voltage-gated ion channels. Although axons are often presumed to faithfully transmit spikes with uniform velocity, conduction velocity often depends on the history of axonal activity on both fast and slow time scales. Thus, spike patterns generated at one end of the axon can change dramatically during propagation to the other end, potentially affecting neural coding. In addition, the degree to which axons contribute to the shaping of activity can depend on neuromodulators like dopamine or serotonin. Additionally, changes in axon excitability and propagation are widely used as diagnostic tools for peripheral neuropathies, commonly associated with dysregulation of ion channels. Yet, these measurements do not take into account how the natural temporal patterns of spikes are changed as they propagate along the axon. In sensorimotor systems, highly repetitive spiking is prevalent. During ongoing repetitive activity, history-dependence can occur with large time scales and, in turn, have distinct effects on shorter time scale dynamics like the frequency-dependence of propagation speed. Here, for the first time, we propose to develop a conceptual description of the history-dependence of axonal propagation, its modification by modulators and its influence on the neural code. Crustacean axons provide several experimental advantages to this end: they allow for multiple long-lasting electrophysiological recordings from different sites are amenable to voltage-clamp measurements, have a well-described range of natural activity patterns, readily follow artificially imposed patterns and share with mammalian axons in their constituent ion channels and activity-dependent dynamics of propagation. Furthermore, the motor patterns they are involved in are well defined and straightforward to monitor. Biophysical and pharmacological methods will be used to establish the types and properties of different ionic currents in these axons. Multiple-site electrophysiological recordings and imposed stimulation patterns will be used to establish the history- and frequency-dependence of propagation over multiple time scales, and their dependence on different ionic mechanisms and neuromodulators. Computational models will be constructed to aid in understanding the non-linear interactions between different ionic mechanisms. A mathematical decoding framework will be developed to produce a description of history- dependence that can be generalized for comparison between different axons, treatments and pathological conditions. Finally, a combination of experimental and theoretical methods will be used to characterize how axon dynamics affect neural coding, specifically how they change motor output and muscle dynamics.

Neuromodulators provide flexibility for neural circuit operation and behavior. Yet, at any given time, neural circuits are subject to modulation by multiple neurotransmitters and neurohormones. Each modulator elicits its own specific activity pattern, and presumably, co-modulation by multiple substances increases the degree of circuit flexibility. Despite the multitude of possible combinations and relative concentrations, the output of any neural circuit has low variability across individuals under baseline conditions. Even under identical modulatory conditions this would not be obvious, given that the expression levels of the molecular targets of modulators, for example ion channels, can vary substantially across the population. Numerous studies show that multiple modulators can target the same voltage-gated ion channel type or the same synapse. We propose, somewhat counterintuitively, that the presence of multiple convergent neuromodulators at low concentrations in fact reduces population variability of circuit activity, a hypothesis that is supported by preliminary data. We further propose that consistent circuit activity can occur in the presence of different sets of convergent modulators. We examine these hypotheses in the oscillatory pyloric circuit of the crab stomatogastric ganglion (STG), one of the premier systems for the study of neuromodulation. We propose to combine detailed quantitative measurements of circuit output, as well as underlying synaptic and voltage-gated ionic currents, at different concentrations of 5 neuropeptide modulators and a muscarinic agonist. The modulators of interest are known to target the same fast low-threshold voltage-gated inward current, which increases excitability of STG neurons. A subset of the peptide modulators are known to enhance the same synaptic connections, while others have unknown actions on the synapses, which we plan to explore. Electrical coupling conductances also appear to be modulated by the peptides, potentially with nonlinear interactions. We propose experiments to examine the interactions of modulators at these component levels, with a detailed focus on two well studied neuropeptide modulators, proctolin and the crustacean cardioactive peptide. We will use evolutionary algorithm optimization techniques to produce populations of computational models of the pyloric neurons and synapses, based on these data, where each single model produces the same responses, but different models in the population have different levels of ionic conductances, as observed in the biological system. Component models will be used to build circuit models that produce appropriate activity and correct (co-)modulatory responses. These models would allow us to explore how circuit-level population variability may be changed by co-modulation and by component variability. Additionally, the models will enable us to predict how modulation of components gives rise to circuit patterns of activity specific to that modulator. This work would provide a basic framework for understanding the interactions between different convergent neuromodulators, which can help elucidate drug interaction mechanisms in pharmaceutical therapies.