Mathematical Neuroscience Seminar

(aka ITEI)

Center for Mathematical Biosciences, Department of Mathematical Sciences

Indiana University Purdue University Indianapolis

This is an informal seminar, free discussion is encouraged and is, frequently, a major component of the seminar.

However, we also have speakers, who will present talks in a more formal way.

Questions: Leonid Rubchinsky

Meeting location and time: HS 4055, conference room at the Center for Mathematical Biosciences at HITS building, (or HS1130, on the 1st floor at HITS) almost every Friday, 1pm, alternate times and locations are indicated in red color.

FALL 2009

October 23, Friday, 3:30pm, LD229 (math department colloquium) 

Karen Sigvardt (University of California, Davis)

Oscillatory Neuronal Networks: mathematical theory and experiments

Abstract

This talk will be devoted to the successive results of mathematical methods in solving the problems of neurobiology of movement. Vertebrate locomotion is controlled by the so-called spinal locomotor central pattern generators (CPGs). Their primary functions are to provide oscillatory motor commands to individual joints or segments and to control the precise timing of those commands across all joints or segments. Our ability to understand the neuronal mechanisms underlying intersegmental coordination has been hampered by the complexity of interconnectivity and the paucity of quantitative data on the magnitude and timing of those connections. Therefore, we employed mathematical approaches to discover general rules by which CPG-like oscillator systems must be constructed to produce appropriate coordinated locomotor behavior. The locomotor CPG is represented as a network of oscillators, in turn represented by ordinary differential equations. Mathematical analysis of such coupled oscillator systems can provide experimentally testable predictions regarding the link between coupling and coordination. I will not assume any neuroscience background for my talk

October 22, Thursday, 2pm, HS1130

Karen Sigvardt (University of California, Davis)

Task related cortical oscillatory activity in Parkinson's disease

Abstract

It has been clearly demonstrated that the pathophysiology of Parkinson's disease (PD) involves changes in oscillatory activity and synchrony among neurons. However few studies have examined task related changes in oscillatory power in PD. We examined responses to a simple button press task in early stage PD subjects and age matched healthy controls. Subjects were shown a visual cue followed by a response target that instructed them to respond with a right, left, or bilateral button press. We used a 275-channel whole-head biomagnetometer to measure fluctuations in oscillatory activity using time-frequency optimized adaptive spatial filtering reconstructions of magnetoencephalography data. PD subjects showed beta activity in additional brain areas (ipsilateral M1S1 and bilateral PPC) in response to a simple button press task. The increase in beta band activity that we observed is consistent with increases in beta band oscillations in the parkinsonian basal ganglia, which has been shown to be correlated with bradykinesia in PD. It is possible that cortical dysrhythmia explains many of the signs of PD

October 14, Wednesday, 2pm, HS4055

Thomas Nowotny (University of Sussex, School of Informatics)

Heteroclinic structures in circuits of Hodgkin-Huxley neurons:
the origin of independent spiking and bursting in neural microcircuits?

Abstract

The relationship between spiking and bursting dynamics has been a key question in neuroscience. Experiments indicate that spiking and bursting dynamics can often be independent. We hypothesize that different mechanisms for spike and burst generation are the origin of this independence. If bursts result from a modulation instability of the network while spikes are produced by individual neurons, the bursting dynamics are independent of the details of the spiking activity. In particular, the slower bursting dynamics could be based on an underlying heteroclinic structure as it has been observed in the Lotka-Volterra rate model. I will discuss the results of a detailed dynamical analysis of a minimal inhibitory neural microcircuit (motif) consisting of three reciprocally connected Hodgkin-Huxley neurons. This high-dimensional system can be reduced to a time-averaged rate model and I will show evidence that the H-H neural network and the rate model have identical bifurcations on the way from tonic spiking to burst generation. Furthermore I will discuss results that indicate that the dynamical structure underlying burst generation is indeed a heteroclinic orbit as in the previous work on the Lotka-Volterra model.

September 25, Friday, 3:30pm, LD229  (math department colloquium)

Jonathan Rubin (University of Pittsburg, Department of Mathematics)

Bursting in Neurons and Networks

Abstract

Neurons are amazing physical structures, capable of generating a wide variety of complex activity patterns. In this talk, after providing a brief introduction to how neurons operate, I will focus on an interesting general form of neuronal activity called bursting, which contributes to a wide range of brain functions. In addition to discussing the functional relevance of bursting, I will show how bursting emerges through the presence of certain features in dynamical systems, such as neuronal models, with two timescales and I will present results on emergent bursting in networks of coupled neurons. I will not assume any background in neuroscience of dynamical systems for this talk.

September 24, Thursday, 2pm, HS1130

Jonathan Rubin (University of Pittsburg, Department of Mathematics)

CAN currents and neuronal bursting in respiration and in the subthalamic nucleus

Abstract

How are rhythmic bursting activity patterns generated in networks of neurons?  There are several qualitatively different mechanisms that can lead to temporally organized bursting in a network.  I will present a recent model of a group-pacemaker network that achieves such bursting in the absence of intrinsic pacemaker neurons.  This model incorporates what is known as a nonspecific cation or CAN current, known to exist in neurons in the mammalian respiratory brain stem.  Interestingly, a related current has been identified in cells in the subthalamic nucleus (STN) of the basal ganglia.  I will present modeling and simulation results suggesting how this current could participate in bursting in the STN and in parkinsonian pathology.

September 11, Friday, 1pm, HS 4055

Joon Ha (IUPUI, Department of Mathematical Sciences and Center for Mathematical Biosciences)

Dynamical properties underlying frequency switching in the two-compartmental model of the dopaminergic neuron

Abstract

Midbrain dopaminergic (DA) neurons display two functionally distinct modes of electrical activity: low- and high-frequency firing. The high-frequency firing is linked to important behavioral events in vivo. However, it cannot be elicited by standard somatic current injection in vitro. A two-compartmental coupled oscillator model of the DA cell that unites data on firing frequencies under different experimental conditions has been suggested. We analyze dynamics of this model. An artificial timescale separation was introduced to simplify the analysis first: the timescale of both somatic and dendritic voltages was made much shorter. By comparison to that, the original case of poor timescale separation was investigated. The high-frequency oscillations of the coupled system were shown to require strong enough nonlinearity of dendritic voltage-dependent currents (folding of dendritic IV characteristics). By its nonlinear voltage dependence, a dendritic N-methyl-D-aspartate (NMDA) synaptic current promotes the high-frequency. Decreasing maximal NMDA conductance lowered the frequency gradually, without complex transitions, by contrast to the case of a poor timescale separation. The inability of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor activation to evoke a high frequency was reproduced regardless of the timescales. However, an elevation in the somatic depolarizing applied current failed to cause depolarization block and evoked a high-frequency under the additional timescale separation. Thus, dynamical mechanisms limiting the frequency under the AMPA and the applied current are different in the model. Taken together, the results explain how structural and temporal characteristics suggested by experimental data contribute to the functional properties of the DA neuron. This is joint work with Alexey Kuznetsov.

SPRING 2009

May 29, Friday, 1pm, HS 4055

Choongseok Park (IUPUI, Department of Mathematical Sciences and Center for Mathematical Biosciences)

Synchronized and nonsynchronized activity in the Basal Ganglia

Choongseok will talk about our recent result on the intermittent synchrony in basal ganglia activity (both experimental data and modeling) and will provide a general overview of the subject.

May 1, Friday, 1pm, HS4055

Journal Club

Novel stimulation of neural circuits

There were two recent papers in Science, dealing with stimulation of neural circuits (to modulate synchronous activity patterns) to improve movement in Parkinson's disease

Optical Deconstruction of Parkinsonian Neural Circuitry by Viviana Gradinaru, Murtaza Mogri, Kimberly R. Thompson, Jaimie M. Henderson, and Karl Deisseroth
Science 17 April 2009: 354-359. http://www.sciencemag.org/cgi/content/abstract/324/5925/354

Spinal Cord Stimulation Restores Locomotion in Animal Models of Parkinson's Disease by Romulo Fuentes, Per Petersson, William B. Siesser, Marc G. Caron, and Miguel A. L. Nicolelis
Science 20 March 2009: 1578-1582.http://www.sciencemag.org/cgi/content/abstract/323/5921/1578

March 27, Friday, 1pm, HS 4055

Giri Krishnan (Department of Psychological and Brain Sciences, Indiana University Bloomington)

Steady State Auditory Gamma Deficits in Schizophrenia: Response Characteristics and Computational Modeling

Abstract

Steady state auditory evoked potential (SSAEPs) in the electroencephalogram (EEG) and magnetoencephalogram (MEG) have been reported to be reduced in schizophrenia, most consistently to frequencies in the gamma range (40 Hz and greater). The current study evaluated the specificity of this deficit over a broad range of stimulus frequencies. SSAEPs to amplitude modulated tones from 5 to 50 Hz were obtained from subjects with schizophrenia (SZ) and healthy control subjects in 5 Hz steps. Time-frequency spectral analysis was used to differentiate EEG activity synchronized in phase across trials using Phase Locking Factor (PLF) and Mean Power (MP) change from baseline activity. Further, a computational model was implemented for test if neuropathological alterations seen in pyramidal cell in schizophrenia could account for the reduced SSAEP responses. Subjects with SZ showed broad band reductions in both PLF and MP with maximal reduction around 40 Hz. The reduction of PLF along with reduced MP reflects the inability to generate gamma frequency oscillation to repetitive auditory stimuli at gamma frequency. The computational model of reduced somal volume without change in dendritic volume of pyramidal neuron resulted in an transient excitation block. The excitation block increases the frequency of spike skipping for periodic inputs, which result in reduced responses to repetitive stimuli. The results from this model fit the experimental findings in schizophrenia and provides further hypothesis for future slice and human experiments.

March 6, Friday, 1pm, HS1130

Yong-Wook Shin (Department of Psychiatry, Indiana University School of Medicine)

Time-frequency analysis of EEG: the brain activity jitters in schizophrenia and schizotypal personality disorder

Abstract

Although schizotypal personality disorder shares some features with schizophrenia including idea of reference or suspiciousness to people, they do not deteriorate to lose the sense of reality. Using time frequency analysis of EEG during an auditory oddball task, the brain response was examined in the patients with schizophrenia and schizotypal personality disorder (SPD). Compared to normal subjects, the patients with SPD showed a deficit only in inter-trial coherence (ITC) of EEG, contrary to the patients with schizophrenia who showed deficits both in the power and ITC. The jittering of brain response as measured by decreased ITC suggests a pathogenesis of SPD.

February 6, Friday, 3pm, HS1130

Charles Wilson (University of Texas San Antonio, Department of Biology)

The generation of natural firing patterns in striatal cholinergic interneurons

Abstract

The spontaneous activity of striatal cholinergic interneurons provides a background release of acetylcholine in the striatum that is critical to maintenance of normal function in that nucleus.  Cholinergic interneurons can fire autonomously in three different spontaneous patterns, even when disconnected from all fast synaptic transmission.  In intact animals, these patterns continue to shape the firing patterns of cholinergic cells and their responses to inputs.  In vivo, the cells respond to salient sensory stimuli with a synchronously pause, presumably producing a decrease in acetylcholine release.  The mechanism of autonomous firing was examined using perforated and whole cell patch recording.  Cellular mechanisms responsible for each of the spontaneous firing patterns were identified, and could be shown to be present in all cells.  Transitions between firing patterns arise from relatively small changes in the balance between ion channel mechanisms.  The ionic mechanisms of spontaneous activity suggest a possible mechanism for the pauses seen in vivo.

February 6, Friday, 1pm, HS1130

Charles Wilson (University of Texas San Antonio, Department of Biology)

Origins of asynchrony in pallido-subthalamic system

Abstract

Neurons of the globus pallidus, substantia nigra, and subthalamic nucleus are all autonomous pacemaker cells that fire tonically, even in the absence of synaptic input.   These cells should be viewed as populations of oscillators, coupled by their synaptic connections, rather than as individual neurons that fire when excited by synaptic input.  This raises the possibility that these cells may signal changes in their input by changing the precise timing of their action potentials, as well as their mean rates. In healthy normal primates and humans, cells in the globus pallidus fire in an uncorrelated way, despite the presence of interconnections among the cells and shared synaptic input.  This suggests the presence of some mechanism of active decorrelation of the cells that counteracts the tendency of coupled oscillators to become phase locked by common input.  In Parkinsons disease and animal models of the disease, pallidal and subthalamic cells show strong correlations, suggesting the loss of this decorrelation mechanism.  Some potential physiological mechanisms for active decorrelation of pallidal cells include mechanisms that cause spike frequency heterogeneity, intrinsic irregularity of neuronal oscillations, and synaptic destabilization of the phase locked state by local interactions.

January 23, Friday, 1pm, HS4055

Journal Club

Seven problems of the basal ganglia

DOI for the upcoming Current Opinion in Neurobiology paper doi:10.1016/j.conb.2008.11.001