Nancy Kopell, Boston University, Department of Mathematics

Rhythms of the nervous system: how to connect biophysics and behavior

One central question of neuroscience is how the properties of the building blocks of the brain (neurons and synapses) can account for the functions of the brain (sensory processing, cognition, and motor control). At the level of individual cells and small networks, there is now a large body of work from anatomy, physiology and genetics about the properties of nerve cells and their connections. But our ability to use that information to get insight into cognition is still in its infancy. This talk outlines a strategy that makes use of the spectral content of the electrical activity produced by the brain. The "rhythms" of the nervous system are combinations of spectral bands that are well-documented to be associated with particular cognitive states (such as attention, active exploration, sleep, etc), and whose relative power changes with learning. Dynamical systems modeling of rhythms is used in several ways to connect the properties of the cells and synapses to mental function. At the lowest level, there is the question of what produces the various spectral bands (and combinations of them) in different neuromodulatory environments; modeling connects the anatomy and physiology of cells and networks to dynamical mechanisms underlying the rhythms. The biophysical and dynamical mechanisms provide clues to how the brain makes use of this temporal structure for particular functions, such as attention and learning. Finally, the pathologies in neural rhythms in various mental illnesses can be connected to pathologies at the cellular level to provide heuristic explanations for why known biophysical changes in these illnesses might give rise to the associated behavioral symptoms. These themes will be illustrated by examples.

Donald Edwards, David Cofer, James Reid, Gennady Cymbalyuk, Ying Zhu

AnimatLab: a simulation tool for closing the CNS-body-world feedback loop

Abstract: Nervous systems function dynamically to control behavior by participating in a feedback loop in which the nervous system commands muscle contractions that propel movement, and movement changes the sensory input to the nervous system from both exteroceptors and proprioceptors. At present, there is no general-use simulator for studying the consequences of this loop on behavior and the nervous system. AnimatLab is a windows-based software environment that we have developed to address this problem. It contains a neural editor for constructing multicompartment and multineuronal models of the neural networks relevant to a behavior under study, a body editor to create a biomechanical model of the body, neural and physics solvers, and 2- and 3-D graphing capabilities for displaying variable time-series, and a 3-D graphical display for observing body motion. AnimatLab can be found at www.animatlab.com and downloaded at www.animatlab.com/newdocs , with the userid animattester and the pword animat. Together with high-speed videography, we have used AnimatLab to study the neural and biomechanical control of a well-characterized system, the locust jump, and we have begun to study postural and locomotor control in crayfish and cats.

Astrid Prinz

Recent findings related to network homeostasis

Neuronal networks, especially central pattern-generating networks (CPGs), usually function reliably throughout life and often show evidence for network homeostasis, i.e. regulation of cellular, synaptic, and network properties that promote stable network function. A number of recent findings, both experimental and theoretical, shed light on possible mechanisms that may underlie activity-dependent as well as activity-independent homeostatic regulation of network output. I will review those findings, focusing on the stomatogastric (STG) CPGs of crustaceans, and will attempt to provide a coherent and up-to-date picture of our current knowledge of homeostatic regulation in the STG.

Vincent Rehder, Liana Artinian, Karine Tornieri, Deb Baro, Kristy Welshhans.
Department of Biology, Georgia State University

Intrinsic and extrinsic modulation of neuronal excitability and growth cone motility by nitric oxide. 

Nitric oxide (NO) is a versatile modulator of various physiological functions. We have shown previously that growth cone motility and neurite outgrowth of a large, identified neuron (buccal neuron B5) is affected by NO and that NO acts via its main receptor, soluble guanylyl cyclase, sGC (Trimm and Rehder 2004; Welshhans and Rehder 2005, 2007). Activation of sGC affects growth cone motility through activation of cGMP, protein kinase G, cADP ribose and calcium release from the endoplasmic reticulum via the ryanodine receptor. Here we report that NO also affects neuronal excitability and investigate the effects of intrinsically produced and externally applied NO on electrical properties using whole cell voltage- and current clamp recordings. B5 neurons grown in vitro for 2 days show spontaneous tonic firing activity and stimulation with NO from the NO donor NOC-7, or from cellular sources, elicits a biphasic response: B5 neurons are initially depolarized and show an increase in firing rate followed by silencing a few minutes later. Using pharmacological inhibitors, a NOS RNAi approach and a neuronal ‘sender-receiver paradigm', we investigate the modulatory role of NO on neuronal excitability. The sender-receiver paradigm (Tornieri and Rehder 2007), in which a B5 cell body is used as a source of NO production (‘sender') and moved up close to a biological tissue (‘receiver'), is a sensitive bioassay to determine physiological effects of NO. We provide evidence that NO is produced constitutively within B5 neurons and serves as an intrinsic modulator of neuronal firing activity. Moreover, we show that neuronal excitability of B5 neurons can be modulated externally by NO release form other cellular sources.
The work was supported by NSF grant 0343096 to VR, a Brains and Behavior grant to VR and DB, and Brains and Behavior Fellowships to KW and KT.

Nadja Spitzer (1)* , Gennady Cymbalyuk (2) , Hongmei Zhang (1) , Donald H. Edwards (1) Deborah J. Baro (1)
(1) Department of Biology, (2) Department of Physics and Astronomy
Georgia State University

Serotonin transduction cascades mediating variable changes in pyloric network cycle frequency in response to the same modulatory challenge

A fundamental question in systems biology addresses the issue of how flexibility is built into modulatory networks such that they can produce context dependent responses. Here we examine flexibility in the serotonin (5-HT) response system that modulates the cycle frequency ( cf ) of a rhythmic motor output. We found that depending upon the preparation, the same 5min bath application of 5-HT to the pyloric network of the spiny lobster, Panulirus interruptus , could produce a significant acceleration, deceleration or no change in steady state cf relative to baseline. Interestingly, circuit output was not significantly different among preparations prior to 5-HT application. We developed pharmacological tools to examine the preparation-to-preparation variability in the components of the 5-HT response system. We found that the 5-HT response system consisted of at least three separable components: A 5-HT 2 b Pan -like component mediated a rapid decrease followed by an increase in cf . A 5-HT 1 a Pan -like component produced a small and usually gradual increase in cf . At least one other component associated with an unknown receptor mediated a decrease in cf. The magnitude of the change in cf produced by each component was highly variable, so that when summed they could produce either a net increase, decrease or no change in cf depending upon the preparation. Overall, our research demonstrates that the balance of opposing components of the 5-HT response system determines the direction and magnitude of 5-HT induced change in steady state cf relative to baseline.

Bill Walthall and Gennady Cymbalyuk, Georgia State University

Dissecting Genetically Locomotion in C. elegans Using Kinematic Analysis

Locomotion in nematodes is characterized by snake-like undulating body waves that propagate from head to tail during forward movement and from tail to head during backward movement. As an innate behavior the investigation of locomotion has provided insight into the relationship between responsible gene and cellular networks. In excess of 100 genes have been identified based upon mutations that interfere with locomotion. We have focused on a subset of these uncoordinated (unc) mutants that effect the development or function of the nervous system. These mutants are either paralyzed or exhibit altered backward movement; rarely are mutants found that affect forward movement. In many cases the genes have been cloned, the product identified and the malfunctioning circuit elements determined. However deductions based upon the circuit alterations suggest that both forward and backward locomotion should be affected. A limitation to the studies is the small size of the animal and its cells, which has restricted the analysis to behavioral rather than physiological measures. Thus the ability to analyze specific contributions of cells, as well as subtle changes that affect the network for forward movement is limited. To address these shortcomings we have recorded spontaneous forward and backward movements of animals expressing green fluorescent protein (gfp) in cells that are positioned equidistantly along the body axis in segmental fashion. Specifically, we used integrated Psur-5: nls::gfp strains expressed in large polyploid nuclei in gut epithelial cells (provided by Hiroshi Qadota and Guy Benian). By capturing points and measuring changes in their position in 300 msec intervals we create kinematic movies and use MatLab for comparison of wild-type and mutant locomotion patterns. M easures were made of changes in interval distance between points on the dorsal and ventral sides of the body, the velocity of wave propagation, the velocity of animal movement as well as parameters of the animal's trajectory. We used the average curvature over all fluorescent cells as an index of overall bending. The sign of the curvature specified the direction of the bending, namely whether the bending is ventral or dorsal For example, if the entire curvature is of the same sign, then the animal is bent in one particular direction, e.g. dorsal. Averaging this index over time gives an indication of whether the animal has a tendency to move symmetrically or asymmetrically. In addition to the previously used measure of the dorsal/ventral ratio, we introduced additional measures based on the Gauss curvature. We will report the results of an analysis of forward and backward locomotion in the following mutants unc-30, which have the cross-inhibitory network inactivated, unc-4, which alters the excitatory drive on ventral but not dorsal muscle during forward and backward movement, and unc-55, which reduces ventral inhibition and increased dorsal inhibition during forward and backward movement . In all three the backward movement is impacted more strongly than forward movement. Kinematic analysis of forward locomotion revealed subtle alterations that had not been identified previously, however forward locomotion is much more resilient to experimental perturbation than backward locomotion. Supported by Brains and Behavior program from GSU.

A. Klishko 1 , D. Coffer 2 , G.Cymbalyuk 2 , D. Edwards 2 , B.I. Prilutsky 1
1. Georgia Institute of Technology, 2. Georgia State University

Role of spinal pattern generator, stretch reflex and muscle properties in the cat paw shake response: A simulation study

A cat paw shake (fast, ~10 Hz oscillations of the limb) is a reflex behavior in response to stimulations of paw skin afferents. It has been shown that both the spinal pattern generator and proprioceptive feedback are involved in generation of rhythmic neural activity in this reflex. For example, rhythmic paw-shake like activity can be elicited in hindlimb muscle nerves of spinal paralyzed animals (fictive paw shake response; Pearson and Rossignol, 1991). In intact animals, the firing rates of primary and secondary spindle afferents during paw shake are several times greater than at rest or in normal locomotion (Prochazka et al., 1989). In this computer simulation study we asked how the spinal pattern generator, spinal reflexes and mechanical properties of muscles could interact and contribute to production of this rhythmic behavior. We developed a computational model of the cat hindlimb and its neural control using AnimatLab, software for modeling and simulations of neurobiomechanical systems. The hindlimb model consisted of 5 rigid segments interconnected by 4 frictionless hinge joints with 11 Hill-type muscles. The muscles were controlled by a simple half-center oscillator and stretch reflex circuits. Forward dynamics simulations reproduced mechanical features of paw shake: fast ~10 Hz oscillations, “amplification” of linear acceleration from proximal to distal segments, and muscle synergies typical for paw shake. Although a realistic paw shake behavior could be produced without stretch reflexes, muscle stiffness in this case would be unrealistically high. Thus stretch reflex appears essential in generation of this rhythmic behavior. Simulations demonstrated also that stretch reflex was capable of reshaping muscle activity from the flexor-extensor synergies typical for locomotion to atypical anterior-posterior muscle synergies observed in paw shake.

Robert Clewley*(1), Erik Sherwood, John Guckenheimer (2)
(1) Georgia State University
(2) Cornell Univerisity

Phase response analysis for coupled bursting neurons

Many basic nervous system functions are controlled by central pattern generators (CPGs) that involve bursting neurons. These neurons alternate between quiescent and active (spiking) states. Of particular interest are mechanisms for establishing and maintaining phase relationships within CPGs, e.g., the motor neuron clusters controlling an animal's left vs. right fore- and hind limbs during walking. To explore these mechanisms using classical phase response curve (PRC) techniques one typically assumes infinitesimal or very weak, finite perturbations. Furthermore, previous analyses of the phase behavior of coupled bursting neurons via coupled PRCs have assumed that the active and quiescent states of individual neurons remain unchanged after synaptic input events. In particular, this presumes only a linear shift in the onset of the active state, within which the number and timing of spikes stays the same. In contrast, we consider realistic perturbations by a single input spike into two types of conductance-based biophysical bursting neuron model, spanning several orders of magnitude in coupling strength. We find that such inputs can potentially add or delete multiple spikes within an active state and significantly alter its inter-spike timing. These effects are highly dependent on the input's phase. To explore this analytically we studied the bifurcations of fast subsystems derived from the full dynamics. Additionally, we use the calculations of "burst phase response" to approximate the slow subsystem's dynamics and intraburst spiking times by a reduced map that predicts the phase behavior of a variety of networks made up of coupled bursting neurons.

Nathan W. Schultheiss , Jeremy R. Edgerton & Dieter Jaeger
Department of Biology, Emory University , Atlanta , GA , USA
Email: nschult@emory.edu

Phase response curve analysis of a globus pallidus neuron model in the presence of randomly timed excitatory and inhibitory synaptic backgrounds  

A phase response curve (PRC) describes the dependency of shifts in spike timing on the phase at which an input occurs within the ongoing inter-spike interval (ISI). We have previously applied PRC analysis to a morphologically realistic GP neuron model exhibiting intrinsically driven rhythmic spiking. Somatic or proximal dendritic inputs resulted in an advance of the next spike that depended on the input phase and amplitude of the input. In contrast, distal dendritic inputs led to a delay of the subsequent spike if an excitatory input was delivered early in the spike cycle.

In vivo, GP neurons are driven to spiking by a balance of excitatory and inhibitory inputs in addition to intrinsic pacemaking mechanisms. To address the question how PRC analysis, which is usually carried out for intrinsic oscillators, may provide insight into in vivo networks of neurons with high ongoing synaptic conductances, we examined phase response behaviors of the GP model in the presence of stochastic background synaptic activity. First, GABAergic and AMPAergic synapses were distributed throughout the morphology of the GP model and activated randomly, resulting in irregular spiking with a mean frequency of 20 Hz. Using 500 separate random synaptic backgrounds, current injection pulses were delivered within the first ISI of each spiketrain, allowing the generation of 500 PRCs. PRCs derived from short and long ISIs (corresponding to fast and slow instantaneous firing rates) were averaged separately and compared to PRCs derived without synaptic background but when the model was driven to similar spike frequencies by depolarizing Eleak.

We find that with synaptic background, PRCs depend strongly on the specific input history in individual spike cycles. However, the average PRC over 500 trials looks similar to the PRC of an oscillator. A significant component of PRC variability with synaptic backgrounds is explained by differences in the duration of interspike intervals. Lastly, for many individual trials there are transient depolarizations that act as trigger points for spike initiation when a test pulse is applied, and triggered spikes can initiate long lasting changes in spike pattern.

Overall, while there is a clear dependence of spike advances or delays on the phase in the spike cycle at which input pulses occur, the average PRC is a poor predictor of the effect of inputs during a specific spike cycle. Thus PRCs constructed for the stochastic background condition should more properly be named pseudo-PRCs. Whether the average pseudo-PRC still predicts phase locking in populations of neurons remains to be determined.

Jianxia Cui* (1) ,  Srisairam Achuthan (2) , Carmen Canavier (2) , Robert Butera (1)

Periodic vs. Transient Estimation of Phase Response Curves

(1) Laboratory for Neuroengineering, Georgia Institute of Technology, Atlanta, GA 30332  (2) Neuroscience, Center, LSU Health Sciences Center, New Orleans, LA 70112

Tzu-Hsin Tsao, Gatech

Applying Biochemical Systems (BST) and Global Optimization Theory in Biological Pathway Construction: Results & Insights

Mathematical modeling of biological systems provides for a mean to make reliable, quantitative predictions of the responses of cells or organisms to experimentally untested situations. Biochemical Systems Theory (BST, the S-system) is a generic approach that can be applied to establish mathematical foundations for all types of biological systems. The basic principle of BST consists of substituting differential equations describing dynamics of variables that change over time with products of power-law functions. BST is more general than linear regression and supports the test for stability, sensitivities, and gains.
Several modeling methodology are explored in the present work. This includes parameter estimation with the Multiple Regression method and the Alternate Regression method based on BST, as well as the traditional Forward Modeling method. Here we seek to improve and extend our previous modeling work on the serotonergic neuromodulatory effect via the PKC-pathway as well as other mechanisms in respiratory-related Hypoglossal Motoneurons (HM).

Tatiana Malaschenko*, Andrey Shilnikov and Gennady Cymbalyuk
Georgia State University

Bursting, tonic spiking, sub-threshold oscillations and silence are basic robust regimes of activity of a single neuron. A model of a leech heart interneuron demonstrates three different types of co-existence: (1) silence and bursting, (2) silence and tonic spiking, and (3) silence and sub-threshold oscillations. We show that these types of co-existence can be explicated by the unstable sub-threshold oscillations (USTO) separating silence and an oscillatory regime and setting the threshold between them. The range of parameters, where the co-existence is observed, is determined by the critical values at which the USTO appear and disappear. More precisely, the USTO occur through the sub-critical Andronov-Hopf bifurcation, where the rest state loses stability. Then, the USTO disappear on the homoclinic bifurcation near which the oscillatory regime disappears as a regime. The bifurcation values are calculated and shown to match the empirical transition values found in numerical experiments in Cymbalyuk et al., 2002.

D.W. Cofer* (1), J. Reid (2), Y. Zhu(2), G. Cymbalyuk (3), W.J. Heitler (4), D.H. Edwards (1)

( 1) Departments of Biology, Georgia State University, Atlanta, GA, USA, 30303
(2) Computer Science, Georgia State University, Atlanta, GA, USA, 30303
(3) Physics and Astronomy, Georgia State University, Atlanta, GA, USA, 30303
(4) School of Biology, Univ. of St. Andrews, Scotland, United Kingdom
Email: dcofer1@student.gsu.edu

Role of the Semi-lunar Process in Locust Jumping

The biomechanical and neural components that underlie locust jumping have been extensively studied. Previous research suggested that energy for the jump is stored primarily in the extensor apodeme and in the semi-lunar process (SLP), a thickened band of cuticle at the distal end of the tibia. As it has thus far proven impossible to experimentally alter the SLP without rendering a locust unable to jump, it has not been possible to test whether the energy stored in the SLP has a significant impact on the jump, or how that energy is applied during the jump. To address problems such as this we have developed a software toolkit, AnimatLab, which allows researchers to build and test virtual organisms. We used this software to build a virtual locust, and then asked how the SLP is utilized during jumping, and how manipulation or removal of the virtual SLP influences jump dynamics. The results show that without the SLP the jump distance was reduced by almost half. Further, the simulations were also able to show that loss of the SLP had a significant impact on the final phase of the jump impulse.

Maria Magdalena Carrasco*, Y.T. Mao, S.L. Pallas
Neurobiology Program at Georgia State University

Adult plasticity in superior colliculus of dark-reared hamsters results from loss of surround inhibition

Cengiz Gunay, Ryan M. Hooper, K. Richard Hammett and Astrid A. Prinz
Biology Department, Emory University

Calcium sensor properties for activity-dependent homeostatic regulation of pyloric network rhythms in the lobster stomatogastric ganglion

Homeostatic regulation has been proposed as a mechanism that can explain the robust behavior of central pattern generating (CPG) neural networks observed experimentally. CPG networks, such as the pyloric network in the stomatogastric ganglion (STG) of the lobster, generate stable patterns of activity in spite of constant molecular turnover and environmental changes. Although the sensing and acting components of regulation are not yet well understood, one likely scenario is that calcium-based activity sensors drive the regulation of intrinsic cellular and synaptic properties. It has been shown that calcium can help maintain stable activity levels in individual model neurons, and pyloric rhythms in one network model. Remaining questions are: (1) whether calcium sensors work in different network model versions, and (2) what intrinsic properties of calcium sensors are important for distinguishing functional from non-functional activity patterns. We tested an existing database of about 20 million simplified pyloric networks, constructed by varying the three LP, PY and AB/PD neuron models and their synaptic strengths, to see if calcium sensors can distinguish functional pyloric activity. Using a set of three sensors---a fast (F), slow (S) and DC (D) sensor---in each neuron, we reached a 88% success rate. Surprisingly, distinguishing the less restrictive set of pyloric-like networks did not achieve a better rate. Nevertheless, networks with non-pyloric tonically firing neurons were easily distinguished. To find properties necessary for these sensors, we constructed a set of 354 sensors with different activation and inactivation rates and sensitivities to calcium. Each of the F,S,D sensors were selected from subsets of these sensors, yielding 85,750 possible F,S,D sensor triplets. Classification performances of pyloric and pyloric-like networks were both normally distributed, reaching a 88.1% success rate. Incorrect classification was often due to high similarity between pyloric and non-pyloric networks. The slow sensors were found to be most important in distinguishing functional networks: an 83% success rate was reached with one in each neuron. We also determined that the classification performance did not increase with different sensors in each cell compared to identical sensors in each cell. Taken together, our results suggest that activity sensing for homeostatic regulation of the pyloric network can potentially be achieved with relatively few, simple calcium sensors and that the properties of these sensors need not necessarily be adjusted to the particular role of each neuron in the network.

Role of synaptic plasticity in the generation of complex patterns and ability to learn by the brain.

Short-term synaptic plasticity contributes significantly to the function of synapses. In particular, basket cells in the hippocampus demonstrate this plasticity in the form of synaptic depression. In addition, basket cell activities have been linked to hippocampal output associated with different behavioral states. Hence, we ( S. Jalil , J. Grigull, and F.K. Skinner) study a two-cell model inhibitory network with short-term synaptic depression. We find that this form of synaptic plasticity endows our network with additional capabilities. In particular, we see novel bursting patterns emerge in the network with synaptic plasticity, which may explain various population activities in the hippocampus.
Long-term synaptic plasticity is thought to be at the heart of complex patterns such as learning and memory. The fact that synaptic connections may be altered and stay altered for a long time has been observed in spike-timing dependent plasticity (STDP) studies. We (D. Standage, S. Jalil , and T. Trappenberg) study learning rules, where we incorporate STDP, in the presence and absence of synaptic saturation. We find that qualitatively both scenarios generate similar dynamics. We also consider nearest neighbor and all-to-all pre- and post-synaptic spike interactions and find no significant difference between the two cases. However, the degree of correlation in the pre- and post-synaptic spike trains impacts the long-term synaptic connections significantly. Frequency dependence of synaptic weight is reversed in the presence of even a small degree of correlation. In particular, we suggest that our synaptic weight curve seen in the uncorrelated spike trains is reminiscent of BCM, rate dependent plasticity, curve.

Ganesh Srinivasamoorthy, UGA

Imaging wave like calcium events in the developing hind brain
of zebrafish

Intercellular calcium waves have several crucial physiological and developmental functions in the nervous system and are of significant interest. Important developmental events like neuronal differentiation, migration, survival and the development of nervous system architecture are believed to be governed by the
precise spatial and temporal distribution of spontaneously propagating calcium waves. Here, we report large scale calcium events, suggestive of spontaneous intercellular calcium waves in the larval zebrafish hindbrain, at the fifth day post fertilization. The
zebrafish imaged were transgenic and genetically encoded with Cameleon, a FRET based calcium indicator. We were able to detect these calcium events using SOARS, a statistical optimization technique, capable of detecting signals from noisy ratiometric
datasets. SOARS detects signals using masks that are weighted dynamically, in a user independent way and retains sharp spatial and temporal intensity changes. Using SOARS, large scale calcium events were observed across the zebrafish hindbrain that were suggestive of calcium waves in the rostro-caudal direction. These wave-like events seem to be generated spontaneously and last for about ~120 seconds.
They also lack any observable periodicity when imaged over a time frame of 60 minutes. Currently, imaging calcium waves in zebrafish has been restricted to embryonic stages with externally injected calcium dyes/ bioluminescent proteins. These techniques have not been successful in exploring calcium waves beyond the embryonic
stages, due to their invasiveness, high noise, poor spatial resolution and other problems. Using cameleon encoded zebrafish and SOARS for data analysis, we were able to overcome the above limitations and were able to observe spontaneous calcium waves in vivo in the developing hind brain of zebrafish.