Mathematical Neuroscience Seminar

Department of Mathematical Sciences

Indiana University Purdue University Indianapolis




FALL 2012


November 16, Friday, 3:30pm, LD229 (math department colloquium, refreshments will be served in LD 259 at 3:00 p.m.

Bard Ermentrout (University of Pittsburgh)

Oscillations, Synchrony, and Disease: What Can Computational Models Tell Us?


In this talk, I will survey several recent results related to the genesis of rhythms in the nervous system, particularly in the so-called gamma range. I will first describe some mechanisms and aspects of rhythms which depend on the interactions between excitatory and inhibitory neurons. Next I will explore what happens when there are changes in the circuitry and some ways in which the rhythms can break down. I will connect this breakdown in rhythms to symptomology in schizophrenia. Finally, I will suggest a new role for oscillations in working memory.



September 21, Friday, 1:00pm, HS4055

Journal Club

The origin of LFP


We will discuss the review Buzsáki G, Anastassiou CA, Koch C. The origin of extracellular fields and currents--EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13:407, 2012. There are also two relatively recent Neuron papers discussing the mecahnisms and spatial extent of LFP signals: Y Kajikawa, CE Schroeder. How Local Is the Local Field Potential? Neuron 72:847, 2011. H Lindén, T Tetzlaff, TC Potjans, KH Pettersen, S Grün, M Diesmann, GT Einevoll. Modeling the Spatial Reach of the LFP. Neuron 72:859, 2011.





April 13, Friday, 10:00am, SL108  (Thesis defense)

Andrey Dovzhenok (IUPUI)

Mathematical models of basal ganglia dynamics

PhD These defense


March 9, Friday, 1:00pm, HS4055

Andrey Dovzhenok (IUPUI)

Exploring Neuronal Bistability at Depolarization Block


March 2, Friday, 1:00pm, HS4055

Andrey Dovzhenok (IUPUI)

The failures of delayed feedback to desynchronized neural oscillations


February 17, Friday, noon,  BS2003 (joint seminar with Bio-Mathematics seminar and iM2CS)

Alexander Niculescu (IU School of Medicine)

Personalized Medicine in Psychiatry: Tracking the Mind to Improve Lives


We are using genomics and phenomics to revolutionize psychiatric diagnosis and treatment. Our approach integrates genetic studies, bioinformatics data mining, predictive tests, and a multidimensional model for mental landscape. A higher degree of mathematization and automation of what we do is a desirable next step.


February 10, Friday, 1:00pm, HS4055 

Journal Club

New insights into the relationship between dopamine, beta oscillations and motor function


We will discuss the review of of Jenkinson and Brown "New insights into the relationship between dopamine, beta oscillations and motor function" Trends Neurosci. 2011 Dec;34(12):611-8.




FALL 2011


November 4, Friday, 1:00pm, HS4055 

Sungwoo Ahn (IUPUI)

Amphetamine induced alterations of the temporal patterning of intermittent synchronized oscillations in hippocampal and prefrontal circuits


D-Amphetamine (d-AMPH) increases the bioavailability of numerous catecholamines, including dopamine, throughout the brain and modulates neural firing in cortical and subcortical regions. While a complex array of d-AMPH-mediated effects on firing have been reported, less is known regarding how d-AMPH affects the oscillatory properties of cortical circuits. In the current study, we simultaneously recorded local field potentials from electrode arrays implanted in the medial prefrontal cortex (PFC) and hippocampus (HC) of awake freely moving rats treated with saline, 1.0 mg/kg, or 3.3 mg/kg d-AMPH. The fine temporal structure of synchrony in delta, theta, beta, and gamma bands between these brain regions was examined to characterize how phase synchronization was altered by each dose of d-AMPH relative to saline. Differences were observed in the average level of phase-locking and in the variation of temporal patterns of synchrony on short (sub-second) time scales (including the distribution of durations of desynchronization events. In general, treatment with d-AMPH evoked higher levels of phase-locking. While this imperfect phase-locking can be potentially attained with both large number of short desynchronization episodes and small number of long desynchronization episodes, the data are marked by the dominance of short desynchronization episodes. These results suggest that within the HC and PFC, d-AMPH acts to increase synchronized oscillatory activity. The dominance of short desynchronization episodes suggests that the synchrony can be easily destabilized, yet it can be quickly re-established. The ease with which neural circuits can transition between synchronized and desynchronized dynamics may reflect altered information transfer regimes in these circuits and contribute to the spectrum of effects on cognition frequently observed with d-AMPH. This is a joint work with Christopher Lapish and Leonid Rubchinsky.


September 16, Friday, 3:30pm, LD229 (math department colloquium) 

Timothy Lewis (University of California, Davis)

Phase-locking in Networks of Neurons: The Effects of Location of Coupling Between Neurons.


Synchronous oscillatory activity in cortical neuronal networks is thought to play an important role in sensory information processing and cognition.  The mechanisms underlying the synchronous oscillations are not well understood, but networks of electrically-coupled inhibitory neurons appear to play critical roles in generating and maintaining the rhythmic activity. Neurons are spatially extended objects, consisting of a soma, an axon and a dendritic tree.  Most modeling studies that examine phase-locking in neuronal networks use single-compartment models, which neglect the spatial structure of neurons.  In this talk, I analyze idealized models of electrically- coupled inhibitory neurons that include spatial structure, and I show that altering the location of the coupling between neurons can substantially change the stability of phase-locked states.



September 9, Friday, 1pm, HS4055  

Yaroslav Molkov (IUPUI, Department of Mathematical Sciences)

Rhythm generation mechanisms in excitatory neural networks of the brain stem


Abstract: The mechanisms generating neural oscillations in the brain stem (pre-Bötzinger Complex, pre-BötC) that persist after blockade of synaptic inhibition remain poorly understood. Experimental studies in thick medullary slices (~700 μm) from neonatal mice containing the pre-BötC identified two types of pacemakers and proposed two intrinsic neuronal bursting mechanisms that may contribute to rhythm generation in the pre-BötC: one with rhythmic bursting activity based on the persistent sodium current (INaP), and the other involving calcium (ICa) and calcium activated, nonspecific cationic (ICAN) currents (Thoby-Brisson M, Ramirez JM. J Neurophysiol 2001, 86:104-112). Interestingly, only the INaP-dependent bursting mechanism has been found in the pre-BötC within thin (~350 μm) slices from neonatal rats (Koizumi H, Smith JC. J Neurosci 2008, 28:1773-1785). Both these mechanisms were also suggested to contribute to the generation of rhythmic activity in the isolated spinal cord. However, an involvement and relative roles of these mechanisms in the operation of rhythmogenic excitatory networks within the brain stem respiratory and spinal cord locomotor central patter generators are still under debate. Studies of the effects of pharmacological blockers of INaP and/or ICAN on the network busting activity and its characteristics (burst frequency, amplitude, and duration) have shown inconsistent results. Therefore, in this theoretical/modeling study we have investigated rhythmogenic mechanisms in a population of excitatory neurons with INaP, ICa and ICAN conductances randomly distributed within the population. In addition, we incorporated in the model and investigated the possible roles of Na+/K+ pump, IP3-dependent intracellular calcium release, and mutually excitatory synaptic interactions within the population in generation of population busting activity. We have demonstrated that such population can operate in several regimes of oscillatory bursting activity, which can be dependent on INaP and/or ICAN, or independent of both. The particular oscillatory regime also depends on several external and internal parameters, such as those defining general neuronal excitability, mutual neuronal interactions including the number of neurons involved (which may vary for example with the size of the slices studied experimentally) and the state of particular ionic conductances. The existence of multiple oscillatory regimes and the transitions between them may provide explanations for the different rhythmogenic mechanisms inferred to operate under various experimental conditions in vitro.







April 1, Friday, 1pm, HS4055 

Journal Club

Reinforcement learning and decision-making in basal ganglia

We will go over a recent review in Neural Computation
Integration of Reinforcement Learning and Optimal Decision-Making Theories of the Basal Ganglia"

by Rafal Bogacz and Tobias Larsen (Neural Computation April 2011, Vol. 23, No. 4: 817–851




February 25, Friday, 1pm, HS4055  

Sungwoo Ahn (IUPUI, Department of Mathematical Sciences)

Describing the temporal structure of intermittent phase-locking


As the coupling between oscillators varies, the oscillatory networks may enter a state, where their dynamics is intermittently synchronized. In particular, this kind of dynamics (intermittent phase-locking) was observed in the oscillatory activity in the basal ganglia of parkinsonian patients. We consider an approach to quantitatively describe this behavior. While synchrony is not an instantaneous phenomenon, when some level of synchrony is present (some preferred angle of phase-locking is present), we can trace the dynamics on each cycle of oscillations, exploring whether it is in synch or out of synch. We apply the method to several simple and standard model systems (couple maps, where  the synchronization manifold and lyapunov exponents are easily computable; coupled Rossler oscillators and Lorenz oscillators exhibiting standard types of intermittency near onset of synchrony) and more complicated models (coupled conductance-based neuronal models) and discuss what this approach reveals about the synchrony in the data and underlying dynamics in the phase space.



February 7, Friday, 1pm, HS4055 

Journal Club

Basal ganglia physiology in motor control

We will go over a recent review in Curr Opin Neurobiol
"Basal Ganglia contributions to motor control: a vigorous tutor"

by RS Turner and M Desmurget, (Current Opinion in Neurobiology 20(6), December 2010, 704-716)




FALL 2010


November 19, Friday, 1pm, HS 4055

Christopher Lapish (IUPUI, Psychology Department)

Analyzing neural activity in the rodent from a dynamic systems approach- what can we learn about cognition?


Serial analysis of individual neurons has not been able to convincingly describe how complex forms of cognition are encoded. Improved data acquisition techniques now allow for large populations of neurons to be recorded simultaneously.  Dynamics systems approaches are revealing how the integrated population dynamic changes across neural populations. This talk will focus on how the population dynamic is altered with cognitive performance in the rat.



October 7, Thursday, 11:45am, HS 4055  (please note unusual day and time of the talk)

Theoden Netoff (University of Minnesota)

Neuronal entrainment by deep brain stimulation for treatment of epilepsy and Parkinson's disease


Deep brain stimulation (DBS) is used for treatment of neuronal disorders such as Parkinson's disease and epilepsy.  The mechanism by which deep brain stimulation affects the nervous system is still not well understood.  It is generally believed that a DBS stimulus elicits action potentials from neurons near the electrode.  However, if a population of neurons is already oscillating, as may be found under pathological conditions such as Parkinson's disease, the periodic stimulation can entrain a population.  The region around the electrode that can be entrained may be much larger than the region of superthreshold stimulus.  We use coupled phase oscillator theory to explain how and when neurons will entrain to a periodic stimulus waveform.  Given this model, it is then possible to optimized a stimulus waveform to maximize disruption or entrainment of a neuronal population.



September 24, Friday, 1pm, HS4055  

Denis Zakharov (Institute of Applied Physics, Russian Academy of Sciences)

Phenomenological modeling of neurons as self-oscillating systems


Application of nonlinear dynamics approach for modeling of neurons as self-oscillating system will be considered. The presentation consists of two parts. The first part is about synchronization of inferior olive cells, the second one concerns modeling of dopaminergic (DA) neuron dynamics. All models are phenomenological.


We have studied synchronization in a system of two interacting inferior olive cells. The interesting experimental fact is that coupling between the cells is electrical but it can be broken under the certain condition for a time interval. Thus besides strength the coupling also has parameters describing time delay (between the instant of cell spike generation and the decoupling) and coupling break duration. Depending on the parameters, the system gives rise to various synchronization regimes and regimes of oscillation suppression. It has been shown shown that even small change of decoupling delay is able to significantly affect the regimes of synchronization between interacting neurons. It makes this parameter very useful for controlling behavior of coupled inferior olive cells.


We have constructed the two compartment model of DA neuron based on modified FitzHugh-Nagumo oscillators with Ca2+-dependent potassium current for each compartment. The compartments correspond to the soma and dendrite and differ in the values of small parameters. We have been studying the mechanism underling high frequency DA neuron activity initiated by external stimuli.   It has been shown that the Ca2+-dependent potassium current plays a key role in DA neuron dynamics and determines the differentials between various stimuli.



September 17, Friday, 1pm, HS4055  

Sungwoo Ahn (IUPUI, Department of Mathematical Sciences)

A mathematical model for odor discrimination


The honeybee antennal lobe (AL) provides an ideal system to study the olfactory system because it is anatomically and genetically simpler than the olfactory bulb of mammals. While anatomical structures within the AL are relatively well known, their functional roles in sensory processing remain poorly understood. Several studies showed that the dynamic processing in the AL may serve to decorrelate sensory representations through early transients rather than by reaching a stable attractor (Mazor et al., Neuron, 2005). Recently, Broome et al. (Neuron, 2006) showed that when two odors are presented with some time gaps, there is a smooth divergence from detecting the first odor and then a smooth convergence to detecting the second odor. Fernandez et al. (J. Neurosci., 2009) showed that there is a smooth transition in the time-dependent neural representation of the cells in response to a smooth transition in the ratios of components in the binary mixtures. We propose a mathematical model for this olfactory system to reproduce several experimental results in the AL such as a smooth transition and a smooth divergence of firing patterns in response to mixtures. We find that synaptic/non-synaptic plasticity helps to discriminate odorants and to reproduce realistic results mentioned above.








April 30, Friday, 1pm, HS4055  

Andrei Dovzhenok (IUPUI, Department of Mathematical Sciences)

Tremor-like oscillations in the model of the basal ganglia-thalamo-cortical loop


The exact origin of the tremorgenesis in Parkinson's disease remains unknown. Although activity within subthalamo-pallidal circuits of basal ganglia and thalamic activity in response to pallidal input (as well as cerebellar involvement) were hypothesized to play a role in the origin of tremor, many experimental results provide the support for the significance of the basal ganglia–thalamo-cortical loop mechanism in the origin of parkinsonian tremor. We consider a conductance-based model of subthalamo-pallidal circuits embedded into a simplified representation of thalamocortical circuit to investigate the dynamics of this loop. We vary the strength of dopamine-modulated connections in the network (to represent the decreasing dopamine level in Parkinson's disease) to simulate the occurrence of the burst firing in the basal ganglia, similar to those observed in patients with Parkinson's disease. The bursting disappears, when the connections are modulated back to represent a higher level of the dopamine (as it would be the case for the dopaminergic therapy), as well as when the thalamocortical feedback is broken (as it would be the case for the ablative anti-parkinsonian surgeries). The model provides a theoretical framework to study a plausible mechanism of the Parkinsonian tremor origin and the ways to suppress it.



April 9, Friday, 3:30pm, LD229 (math department colloquium) 

Maxim Bazhenov (University of California, Riverside)

Mathematical Modeling of Potassium Dynamics in Epileptic Cortex


Epilepsy is traditionally associated with pathological excitability of neuronal populations in the cortex. One of the factors affecting excitability is the extracellular ion concentrations. While experimental approaches are limited in their ability to shed light on the dynamic feedback interaction between ion concentration and neural activity, mathematical models and dynamic system theory provide powerful tools to study activity-dependent modulation of intrinsic excitability mediated by extracellular ion concentration dynamics. In this talk I will present an example of how numerical results and detailed bifurcation analysis of the model may explain some potential mechanisms of the generation of epileptic seizures.



March 12, Friday, 1pm, HS4055 

Journal Club

Temporal interactions between cortical rhythms

We will go over a paper in Frontiers of Neuroscience:
"Temporal interactions between cortical rhythms"

by AK Roopun, MA Kramer, LM Carracedo, M Kaiser, CH Davies RD Traub, NJ Kopell and MA Whittington



February 12, Friday, 3:30pm, LD229 (math department seminar) 

Yi Sun (SAMSI)

Network Dynamics of Hodgkin-Huxley neurons


The reliability and predictability of neuronal network dynamics is a central question in neuroscience. We present a numerical analysis of the dynamics of all-to-all pulsed-coupled Hodgkin-Huxley (HH) neuronal networks. Since this is a non-smooth dynamical system, we propose a pseudo-Lyapunov exponent (PLE) that captures the long-time predictability of HH neuronal networks. The PLE can capture very well the dynamical regimes of the network. Furthermore, we present an efficient library-based numerical method for simulating HH neuronal networks. Our pre-computed high resolution data library can allow us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations. By using the library-based method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity. Moreover, our large time steps using the library method can overcome the stability requirement of standard ODE methods for the original dynamics.



January 29, Friday, 1pm, HS4055 

Journal Club

Basal ganglia dopamine and motor behavior/action selection

We will go over two recent reviews, published in Current Opinion in Neurobiology:

"The dynamics of dopamine in control of motor behavior" by Mati Joshua, Avital Adler and Hagai Bergman
Current Opinion in Neurobiology Volume 19, Issue 6, December 2009, Pages 615-620

"Dopamine and synaptic plasticity in dorsal striatal circuits controlling action selection" by D James Surmeier, Joshua Plotkin and Weixing Shen
Current Opinion in Neurobiology Volume 19, Issue 6, December 2009, Pages 621-628



FALL 2009


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

Karen Sigvardt (University of California, Davis)

Oscillatory Neuronal Networks: mathematical theory and experiments


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


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?


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


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


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


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.







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.

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.



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


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


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


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


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    





FALL 2008


December 5, Friday, 1pm

Jean-Philippe Thivierge (Indiana University Bloomington, Department of Psychological and Brain Sciences)

Synchronization in the Brain: Deciphering the Development, Damage, and Recovery of Neural Interactions


The spontaneous synchronization of groups of cells plays an instrumental role in the activity-driven development and functionality of cortical neural circuits. However, despite its established behavioral and cognitive roles, the cellular mechanisms underlying neural synchronization remain poorly understood. In particular, the natural tendency of cells to synchronize their activity without any apparent periodicity cannot be explained by simple oscillatory mechanisms, including attractor models. In this talk, I will propose a computational model based on recurrent circuits of heterogeneous cells (where different neurons possess different intrinsic properties) that captures the nonperiodic nature of synchronization in addition to other key properties. Beyond replicating functional interactions in healthy cortical networks, computational simulations also examine neuroprotective factors that preserve these interactions in the event of neural injury. In the model, damages to the functional interactions among cells are prevented by increasing baseline activity across the whole population. Evidence supporting this prediction was obtained by recording from cultured cortical neurons interfaced with 64-electrode arrays, and inducing oxygen-glucose depravation (OGD). When preconditioning cells with AP4/bic, leading to an increase in baseline activity, functional interactions were resistant to OGD, and normal synchronization was preserved. Taken together, these computational and experimental results further our understanding of functional interactions in healthy cortical networks and open new areas of exploration into neuroprotective factors for ischemic stroke.



November 7, Friday, 3:30pm, LD229 (Math department colloquium)

David Terman (Ohio State University, Department of Mathematics and Mathematical Biosciences Institute)

Neuronal Dynamics and Basal Ganglia


The basal ganglia are a group of nuclei that play an important role in the generation of movement. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have, in fact, been the target of recent therapeutic surgical procedures including deep brain stimulation. Numerous experiments have demonstrated that neurons within the basal ganglia display a variety of dynamic behaviors; moreover, patterns of neuronal activity differ between normal and pathological states. Neither the origins of these neural firing patterns nor the mechanisms that underlie the beneficial effects of deep brain stimulation are well understood. In this lecture, I will describe a recent model for neuronal activity within the basal ganglia. Geometric dynamical systems methods will be used to analyze the activity patterns. I will then discuss how the model has been used to propose mechanisms underlying the beneficial effects of deep brain stimulation.



October 24, Friday, 1pm, HS4055

Alexey Kuznetsov(IUPUI, Department of Mathematical Sciences and Center for Mathematical Biosciences)

Multiple mechanisms for artificial genetic oscillations


Regulatory molecular networks have numerous pharmacological and medical applications. The oscillatory mechanisms and the role of oscillations in these regulatory networks are not fully understood. In this presentation, I explore two oscillatory mechanisms: the hysteresis-based relaxation oscillator and the repressilator. We combine these mechanisms into one regulatory network so that only two parameters, the strength of an additional regulatory connection and the timescale separation for one of the variables, control the transition from one mechanism to the other. Our data supports a qualitative difference between the oscillatory mechanisms, but in the parameter space, we found a single oscillatory region, suggesting that the two oscillatory mechanisms support each other. We then examine interactions in a basic population: that is, a pair of the composite oscillators. We found that the relaxation oscillation mechanism is much more resistant to oscillatory death as the cells are diffusively coupled in a population. Additionally, stationary pattern formation has been found to accompany the relaxation oscillation, but not the repressilator mechanism. These properties may guide the identification of oscillatory mechanisms in complex natural regulatory networks.



October 10, Friday, 1pm, HS4055

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

Intermittent phase synchronization in the system of bursting inhibitory neurons



September 19, Friday, 1pm, HS4055

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

Roles of Gap Junctions in Neuronal Networks


There is much evidence showing the presence of gap junctions in neuronal networks. We study the roles of gap junctions in the dynamics of neuronal networks in three distinct problems. First, we study the circumstances under which a network of excitable cells coupled by gap junctions exhibits sustained activity. We investigate how network connectivity and refractory length affect the sustainment of activity in an abstract network. Second, we build a mathematical model for gap junctionally coupled cables to understand the voltage response along the cables as a function of cable diameter. For the coupled cables, as cable diameter increases, the electrotonic distance decreases, which cause the voltage to attenuate less, but the input of the second cable decreases, which allows the voltage of the second cable to attenuate more. Thus we show that there exists an optimal diameter for which the voltage amplitude in the second cable is maximized. Third, we investigate the dynamics of two gap-junctionally coupled theta neurons. A single theta neuron model is a canonical form of Type I neural oscillator that yields a very low frequency oscillation. The coupled system also yields a very low frequency oscillation in the sense that the ratio of two cells' spiking frequencies obtains the values from a very small number. Thus the network exhibits several types of solutions including stable suppressed and 1:N spiking solutions. Using phase plane analysis and Denjoy's Theorem, we show the existence of these solutions and investigate some of their properties.



September 12, Friday , 1pm, HS1130   


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

The generation of natural firing patterns in striatal cholinergic interneurons


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.



September 11, Thursday, 1pm, HS1130 (note unusual day of the week)

Yixin Guo (Drexel University, Department of Mathematics)

Modeling Parkinson's Disease and Brain Stimulations


Parkinson's disease (PD) is the result of the loss of dopamine-producing neurons in the basal ganglia. The underlying disorder causing abnormal movements in PD patients is the unfaithful relay responses presented in thalamocortical (TC) cells which receive inhibition from the internal segment of the globus pallidus (GPi) in the basal ganglia. In the past decade, deep brain stimulation (DBS) to the subthalamic nucleus (STN) or other brain regions, through a surgically implanted electrode, has become a widely used therapeutic option for the treatment of Parkinson’s disease (PD). We construct a basal ganglia-thalamocortical network to examine TC relay responses to an excitatory input train under a variety of inhibitory GPi signals obtained from both computations and experimental recordings. We investigate how the changes in GPi activity impact its thalamic targets under three states: normal, parkinsonian, parkinsonian with STN-DBS. Our findings show that inhibition from parkinsonian GPi activity without DBS compromised TC relay of excitatory inputs compared with the normal case, whereas TC relay fidelity improved significantly under the GPi inhibition from therapeutic DBS. These results support the hypothesis that DBS alters parkinsonian GPi activity in a way that may improve TC signal processing. Beyond studying the mechanism of DBS, we further explore other possible closed-loop brain stimulations that can restore TC relay ability by modifying the parkinsonian GPi inhibition.



August 22  

Journal Club

Algebraic structures in music

DOI for the recent Science paper 10.1126/science.1153021 and a commentary 10.1126/science.1155463







April 25

Donald French (University of Cincinnati)

Numerical Approximation of Solutions to Nonlinear Inverse Problems Arising in Olfaction Experimentation


Identification of detailed features of neuronal systems is an important challenge in the biosciences today. An interdisciplinary research team has been working to determine the distributions of ion channels in frog olfactory cilia.  The cilia are tiny tube-like structures that extend from the olfactory receptor neurons. The first step in the transduction of an odor into an electrical signal occurs in the membranes of the cilia and is controlled primarily by the ion channels.

A mathematical model involving integral and partial differential equations is derived to model experiments aimed at identifying features of the distribution of these ion channels.  Numerical and analytical approximations to the model solutions are derived and used with experimental data to obtain estimates of the spatial distribution of the ion channels along the length of a cilium.  The results from this mathematical and experimental study suggest that these channels have a non-uniform distribution.



March 28 

C Park (IUPUI, Mathematics), R Worth (IUPUI Mathematics; IU Neurosurgery), L Rubchinsky (IUPUI, Mathematics; IU Stark Institute)

Oscillations and synchronization in human subthalamic nucleus: theory and experiment



February 29 

Alexey Kuznetsov (IUPUI, Mathematics)

Firing patterns of midbrain dopaminergic neuron: insights from dynamical modeling



February 8  

Journal Club

Effect of weak electric fields on spike timing

The link to the paper is  link to the paper. There is also a letter in J Neurosci



January 18  

Journal Club

Extended analog computers

A preprint can be found here. You can also look at the author's page



FALL 2007


November 16 (HITS 1130)

Journal Club

Local Field Potentials from nonsynchronized neuronal oscillators

Diaz et al paper in J Neurosci.



November 9 (HITS 1130)

Math neuro - Neuroimaging meeting

Leonid Rubchinsky (IUPUI, Mathematics; IU SoM, Stark Institute)

Synchronization patterns in basal  ganglia


October 26

No meeting this day, please come to the Center for Mathematical Biosciences Open House at HITS  noon - 4:30pm




Math neuro - Neuroimaging meeting (math people - Leonid Rubchinsky, Alexey Kuznetsov - will give informal presentation on their research projects)



October 12

Journal Club

Mechanisms of Epileptogenesis II

Bob Worth will discuss some recent issues + sonification of epileptic eeg; sonification papers are added here.



October 5

Journal Club

Mechanisms of Epileptogenesis

Bob Worth will discuss some recent issues; also here are two older papers he suggested.



September 21 Math Dept Colloquium, LD229 4:00pm

Mikhail Rabinovich (University of California, San Diego)

Transient cognitive dynamics, metastability and decision making


The idea that brain cognitive activity can be understood into the conceptual framework of nonlinear dynamics is intensively discussed last fifteen years. One of the popular points of view is that metastable states or cognitive modes are playing a key role in the execution of the cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of the large scale brain networks in the presence some noise. Such transients are the sequential switching between different metastable cognitive states. The main difficulty of the dynamical theory to the understanding of the transient cognitive process is the fundamental contradiction between reproducibility and flexibility of the transient behavior. In this paper we propose a theoretical description of transient cognitive dynamics that based on the interaction of metastable cognitive modes. The mathematical image of such transients is a stable heteroclinic sequence i.e. chain of metastable sets (saddles) connected by unstable trajectories (separatrices). I will discuss the basic mathematical model that is a strongly dissipative dynamical system and formulated the necessary conditions for the robustness and reproducibility of cognitive transients that satisfied the competing requirements for their stability and flexibility. Based on the suggested approach we will consider the effective solution of sequential decision making problem i.e. a simple limited time game: agent is taking sequential actions in a changing noisy environment so as to maximize the cumulative reward.



September 7 HITS1130, note unusual meeting time: 1:45pm

John Beggs (Department of Physics and Biocomplexity Institute, Indiana University Bloomington)

A continuous phase transition in neocortical slice networks


Recent experiments demonstrate that activity in neocortical circuits can propagate in the form of avalanches whose sizes follow a power law distribution, suggesting that these circuits operate near a continuous phase transition point. Computational models indicate that this critical point may be optimal for information processing. However, the existence of a power law is not sufficient to establish critical behavior because stochastic processes that do not undergo phase transitions can also produce power laws. We recorded power law distributions of neuronal avalanches from neocortical slices and then pharmacologically perturbed network activity. We then measured deviations from power law behavior. Here we show that these deviations covaried systematically with a control parameter, as would be expected for a continuous phase transition. A critical branching model captures this transition, while stochastic models do not. Our findings imply that the physical theory underlying continuous phase transitions can be fruitfully applied to neocortical circuits.


August 24 (HITS 1130)

Math neuro - Neuroimaging meeting (an informal presentation on diffusion tensor imaging for math people is planned, Bob has several papers to look at)



August 17

Journal Club

New issues in Deep Brain Stimulation

Review of recent literature, look at the recent Nat Rev Neurosci review






May 18

Math neuro - neuroimaging meeting


May 4

Journal Club (continuation of April 13th)



April 13

Journal Club

Oscillations in LFP recorded in basal ganglia

Leonid Rubchinsky will make a presentation based on current literature


March 2

Journal Club

Small world, scale free and other fancy networks in cortex

The link to the paper suggested by Bob is There are also several related papers by Sporns et al., There is also a commentary by Sporns  and a link to original paper there. And all this is related to a paper we looked at quite a time ago


February 16 1pm SL206

Choongseok Park (Ohio State University)

Irregular Behavior In An Excitatory-Inhibitory Network


The basal ganglia are a group of subcortical nuclei involved in the generation of voluntary movement, cognition and emotion.Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have been the target of recent therapeutic surgical procedures including deep brain  stimulation (DBS). The basal ganglia display complex firing patterns which differ between normal and pathological states. Neither the origins of these firing patterns nor the neuronal mechanisms that underlie the patterns are understood. Conventional theories of basal ganglia are based on the average firing rate of the neurons and ignore the importance of temporal dynamics; they do not explain where tremors come from or why DBS would alleviate the symptoms. In this lecture, I will describe recent progress on the development of more realistic, biophysically based models and review various firing patterns which emerge in those models. I will also discuss geometric dynamical methods for analyzing the irregular activity patterns.


February 2, 2:15pm SL206 (note unusual meeting time)

Jaejoon Lee (Purdue University, Department of Electrical and Computer Engineering)

Consensual and hierarchical classification of remotely sensed multispectral images



January 26

Journal Club

Steven Sandstrom (IU SOM)

Synaptic mechanisms of gamma oscillations in inhibitory interneuron networks (Nature Reviews Neuroscience 8:45, 2007)



January 19 3:30pm

(math dept colloquium)

Andrey Shilnikov (Georgia State University, Atlanta)

Homoclinic chaos on routes into bursting in slow-fast models of neurons


Bursting is a manifestation of the complex, multiple time scale dynamics observed in diverse neuronal models. A description list of the nonlocal bifurcations leading to its onset is far from being complete and presents a dare need for cross-disciplinary neuroscience and the dynamical systems theory. There has been a recent breakthrough in this direction that explains a few novel mechanisms of transitions between tonic spiking and bursting activity, as well as their co-existence in models of leech interneurons through homoclinic saddle-node bifurcations of periodic orbits including a blue sky catastrophe. We will discuss the bifurcation theory that underlies theses transitions, as well as one on a spike adding route: as a parameter shifting the membrane potential of half-inactivation slow potassium current is monotonically changed, a sequence of bifurcations occurs causing incremental change of the number of spikes in a burst.  Of our special interest is the origin of the sequence, where each transition is accompanied by chaos.  To figure out the transition dynamics we construct a one-parameter family of the onto Poincare return mappings on the central manifolds of slow motions. We show that the transitions in question are due to the bifurcations of homoclinics of a repelling point of the map setting a threshold between tonic spiking and hyperpolarized states of the neuron model.



FALL 2006


November  3

Zao (Joe) Xu (Anatomy and Cell Biology, IU School of Medicine)

Excitotoxicity, dopamine and selective cell death after cerebral ischemia


Neurons in the striatum are highly sensitive to cerebral ischemia. Medium spiny (MS) neurons die after transient cerebral ischemia while large aspiny (LA) interneurons survive.  Glutamate and dopamine concentration dramatically increase during ischemia.  Excitotoxicity has been implicated as a major cause of cell death after ischemia. Potassium currents play crucial roles in regulating neuronal excitability and ion homeostasis, which might influence the ischemic outcome.  To reveal the mechanisms underlying the selective cell death, electrophysiological changes in MS neurons and LA neurons were compared before and after ischemia. The excitatory synaptic transmission is differentially altered in striatal neurons after ischemia.  The EPSCs were potentiated in ischemia-vulnerable MS neurons but depressed in ischemia-resistant LA neurons after ischemia.  Dopamine had detrimental effects on ischemic neurons.  Removal of dopamine neurons reduced cell death in the right, but not left striatum. Such asymmetrical protection was associated with D2 receptor up-regulation.  A-type potassium current (IA) is one of the major potassium currents in neurons and is differentially regulated after cerebral ischemia.  The IA increases significantly in large aspiny (LA) neurons in the striatum but not in medium spiny (MS) neurons after ischemia in vivo or in primary culture under oxygen/glucose deprivation (OGD).  The differential increase of IA correlates with the higher resistance of LA neurons to cerebral ischemia.  Increase of IA by recombinant expression of Kv1.4 or Kv4.2 improves the tolerance of MS neurons to OGD.  The increase of IA is correlated with an increase of Kv1.4 expression and the activation of PKCa in LA neurons. These results indicate that the differential up-regulation of excitatory transmission and A-type potassium current in ischemia-vulnerable and ischemia-resistant neurons might contribute to the selective cell death



October 20

Journal Club

Bob Worth (Indiana University School of Medicine - IUPUI) will talk about

Nonlinear dynamics of networks: the groupoid formalism

Several relevant papers: Golubitsky & Stewart Bull. Amer. Math. Soc. 43:305, Stewart Nature 427:601, and see some stuff here



October 6 This talk will be at 1pm at LD030

Baltazar Aguda (Mathematical Biosciences Institute, Ohio State University)

Analysis of networks of oncogenes and tumor-suppressor genes involved in cell cycle checkpoints, apoptosis, and cell survival

The slides for the talk are available here, as a power point presentation (760K).


Oncogenes and tumor-suppressor genes promote and inhibit, respectively, the progression of carcinogenesis.  Networks of interactions among these genes in the G1 cell cycle checkpoint (called the Restriction Point), in the regulation of cell death (apoptosis), and in survival signaling pathways will be illustrated.  Modularization and qualitative stability analysis of these networks allowed us to reduce their complexity and to identify key control motifs.  In the G1 checkpoint, the positive feedback loops in the interactions among Cdc25A, p27Kip1, and CDK2 generate an instability that can explain the switching behavior associated with the Restriction Point.  Recent work on the cross-talk between p53 and Akt, which led to a proposed cell survival-death switch, will also be presented.



September 29

Journal Club - informal meeting -discussion of brain machine interfaces

recent review on brain machine interface by Lebedev and Nicolelis availalble through sciencedirect at



September 22

David Green (NeuroPace, Inc)

Responsive Neurostimulator System (RNS)

Indiana University is participating in a clinical trial of a novel approach to the treatment of refractory epilepsy. The RNS is the first fully implantable closed-loop system designed to detect and stimulate the neuronal hypersynchrony that occurs in epilepsy. A review of literature supporting a closed-loop system will be provided. In addition, the diagnostic capabilities of the RNS will be presented for researchers
interested in analyzing the long-term ECOG and diagnostic data the RNS provides. The RNS is an investigational device that has not been proven safe or effective and is limited by United States law to investigational use.



September 15

Journal Club

recent review on brain machine interface by Lebedev and Nicolelis
availalble through sciencedirect at



August 25 

Informal meeting, we'll finish discussion of July 7 topic





August 18 

we'll continue discussion from the previous week


August 11 

Journal Club - Desynchronization by deep brain stimulation: theory and experiment.

Some refs (Tass and colleagues, Pikovsky & Rosenblum) are here


July 7

Journal Club

Bob Worth (IUSM-IUPUI) will talk about

connection between intracellular and extracellular action potential waveform

Links to several relevant papers: Gold et al On the origin of the extracellular action potential waveform: A modeling study J Neurophys 95:3113 ;

Holt & Koch Electrical interactions via the extracellular potential near cell bodies J Comp Neurosci 6:169


June 16, 3pm

This is a one-time deviation from math neuro and biodynamical spirit of the seminar

Student talk

Zack Schaub (IUPUI)

The dynamical origin of oscillatory behavior in business cycles in supply netowrks.



May 26, 3pm

Niels Porksen (Eli Lilly)

Pulsatile insulin secretion as a marker of pre-diabetes: using a mathematical model.


May 17

journal club

Glycolitic oscillations etc (some references are Tsaneva-Atanasova et al; Rudic et al., one more and yet another)




May 5

Alexey Kuznetsov (Math, IUPUI)

Cell cycle and circadian clock oscillators (review of the recent literature)


April 14

journal club

Again: origin of EEG and LFP


April 7

journal club

Alexey Kuznetsov

Voltage-calcuim-glucose oscillations in β-cells.



March 3

(departmental colloquium)


Eugene Izhikevich, The Neurosciences Institute, San Diego, CA


Polychronization: Computation With Spikes


Time: 3:30 pm (pre-colloquium tea time in math department at 3pm, LD 259), Room: LD229



Polychronization is the ability of a spiking network to exhibit reproducible time-locked but not synchronous firing patterns with millisecond precision. It is a generalization of the phenomenon of synchronization, and it may play an important role in information processing by the brain. Simulations of realistic spiking networks show that neurons often spontaneously self-organize into groups and generate patterns of stereotypical polychronous activity. To our surprise, the number of co-existing polychronous groups far exceeds the number of neurons in the network, resulting in an unprecedented memory capacity of the system. We speculate on the significance of polychrony to the theory of neuronal group selection (TNGS, Neural Darwinism), cognitive neural computations, binding and gamma rhythm, mechanisms of attention, and consciousness as "attention to memories". This talk is based on the recent paper published in Neural Computation and available at


February 17

Janet Best, Mathematical Biosciences Institute, Ohio State University

A minimal neuronal model that separates frequencies


Neuronal systems receive inputs from other structures, transform these signals, and then pass the processed signals onto other brain areas. The nature of these transformations and their roles in information processing are poorly understood. Motivated by experiments demonstrating that the olfactory bulb separates odor representations, we seek a minimal biological model of a neuronal system that can separate a mixture of incoming signals. As a first step, we consider inputs that are the superposition of two periodic spike trains. We ask what network properties would allow the system to separate the two frequencies; that is, some of the output cells should fire at one of the incoming frequencies and other output cells should fire at the second frequency. We present and analyze a simple neuronal network that is remarkably successful at separating frequencies. Our analysis uses methods from discrete dynamics and the geometric theory of singular perturbations.


February 3

Ray Chin, Math, IUPUI

Considerations of numerical integration of multiple scales problems


January 27

Pedro P. Irazoqui and Jenna L. Rickus, Purdue University, Weldon School of Biomedical Engineering

Brain-Computer Interfaces for Epilepsy


Systems made up of sensing, actuating, transmitting and powering modules, combined into distinct, application-specific integrated-circuits and devices, are enabling researchers and clinicians the maximum flexibility in conducting meaningful and hereto impracticable experiments. These systems are also developing novel avenues for the treatment of neural disorders through miniature, wireless, electronic prostheses. The important parameters and trade- offs in the design of the individual modules, their integration into functioning systems, and the manner in which they interface both with the biology and the external world are presented in theory and in practice, with specific research and clinical application to epilepsy.


January 20

journal club

Origin of local field potentials in cortex and basal ganglia

(some reading is here )



FALL 2005

November 18

Alexey Kuznetsov - IUPUI

Neural Networks and heteroclinics II

We'll continue to talk about heteroclinic orbits and neural networks. Alexey will talk about some of his recent results


November 11

journal club

Leonid Rubchinsky IUPUI-IUSM

I'll talk about winnerless competition and heteroclinics following recent papers of Mikhail Rabinovich.



September 30

1pm, LD004 - please, note this is not our usual meeting place (math neuro seminar / math dept colloquium)

Georgi Medvedev (Drexel University, Dept of Mathematics)

Using one-dimensional maps for analyzing neuronal dynamics

Understanding mechanisms for patterns of electrical activity of neural cells and principles for their selection and control is fundamental for determining how neurons function. After a classical series of papers by Hodgkin and Huxley nonlinear differential equations became a common framework for modeling neurons. The bifurcation theory for nonlinear ordinary differential equations provides a powerful suite of tools for analyzing neuronal models. Many such models reside near multiple bifurcations. Consequently, in using bifurcation analysis one often encounters rich and complicated bifurcation structure. Therefore, it is desirable to distinguish the universal features pertinent to a given dynamical behavior from the artifacts peculiar to a particular model. This is important in view of the unavoidable simplifications one makes in the process of modeling such complex systems as neural cells, and under the conditions when many parameters are known approximately. The goal of this talk is to describe some general traits of the bifurcation structure for a class of models of excitable cells. They follow from the generic properties of two-dimensional flows near a homoclinic bifurcation. We present a method of reduction of a model of an excitable cell to a one-dimensional map. The bifurcation structure of the system with continuous time endows the map with distinct features: it is a unimodal map with a boundary layer corresponding to the homoclinic bifurcation in the original model. The qualitative features of this map account for various periodic and aperiodic regimes and transitions between them. Our approach retains the biophysical meaning of the parameters in the process of reduction, which allows for precise interpretation of various dynamical patterns.


September 23

Robert Worth (IUSM- Neurosurgery, IUPUI-MATH) and Richard Friedman (IUSM-Neurosurgery)

will give an informal talk about microtubules


September 16

Anna Kuznetsova

This is the continuation of the previous talk, which will be finished in 30 min, so that interested people can attend colloquium at 1:30.

Anna will be available after the talk for discussion.


September 9

Anna Kuznetsova (Dept of Nonlinear Processes, Saratov State University)

Modeling new mechanism of dopamine regulation of cortical functions (attention, working memory).


Recent studies have described the impairment of synchronized gamma frequency neuronal firing oscillations in mental diseases. Several studies, in humans, have also demonstrated a significant reduction in the intensity of attention-related gamma oscillations with drugs affecting D4-type dopamine receptors. D4 receptors have the unique ability to carry out phospholipid methylation, in which the insertion of methyl groups increases the spacing between membrane phospholipids. Impaired phospholipid methylation has been documented in different mental diseases. We have proposed a new mechanism and numerically examined how dopamine-induced phospholipid methylation can affect the firing activity of a cortical neuron due to the sensitivity of different ion channels to their membrane environment. We evaluate the proposed mechanism via consideration of pyramidal cell-interneuron networks to reveal the main neuronal membrane components as well as network elements responsible for enhancement of gamma oscillations. Our observations coincide with recent experimental MEG recordings of gamma oscillations, where the main contribution comes from principal cell activity. Dynamics of these networks has been studied at different conditions according to data on human neurons. The conditions for regular spiking principal neurons to produce a self-terminating spike trains, which are related to short-term memory function, under neuromodulatory control has been studied as well. We examine whether dopamine-induced phospholipid methylation can contribute to the modulation of cortical activity (attention, working memory) by increasing firing rate and affecting spike train. We show that specific anatomical connections within the neural network influence the effect of dopamine, and dysfunctional phospholipid methylation can lead to impaired neural synchronization.

This is joint work with R.C. Deth, Department of Pharmaceutical Sciences, Northeastern University.


September 2

Leonid Rubchinsky (MATH-IUPUI; Stark Institute - IUSM)

Oscillatory death in chains and small-world networks of oscillators II

this is the continuation of my previous talk


August 24

1pm, LD004 (please, note this is not our usual meeting place)

Leonid Rubchinsky (MATH-IUPUI; Stark Institute - IUSM)

Oscillatory death in chains and small-world networks of oscillators


Following persistent requests of Michael Frankel I will talk about my past work on oscillatory death in chains of oscillators and its destruction by spatial disorder. I will follow with some recent results on similar effects in small-world networks.



August 19

1pm, LD004 (please, note this is not our usual meeting place)

Alexey Kuznetsov (MATH-IUPUI)

Localization of activity in coupled oscillators:
a mechanism for NMDA-activated high-frequency firing in dopamine neuron.


Mesencephalic dopamine neurons ordinarily will not fire faster than about 10/s in response to somatic current injections. However, in response to dendritic excitation, much higher rates are briefly attained. In an analysis of a simplified biophysical model, we suggest a way such high-frequency transient firing may be evoked. Our model represents the neuron as a number of electrically coupled compartments with different natural frequencies, which correspond to the soma and parts of the dendrite. We reduce this model, substituting all the diversity of the compartments that describes real dendritic geometry by a pair of compartments: the slowest, somatic and the fastest, the most distal dendritic one. We have shown that, in the absence of any synaptic stimulation, oscillatory pattern in this model is controlled by the somatic compartment, and, therefore, has a very low frequency. We consider and compare NMDA and AMPA activation applied to the dendritic compartment. Our main result is that activation of the dendritic NMDA receptors evokes oscillations at a much higher frequency. We have also shown that dendritic AMPA activation, by contrast, cannot increase the frequency significantly. The major dynamical question left is how the dendritic frequency can dominate during the application of NMDA. We employ a phenomenon of localization to explain this behaviour.





May 27

Dynamics of brain during epilepsy.

Bob Worth suggested the reading: Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng. 2003 May;50(5):540-8. Review.


May 20

We do not have any specific neuroscience topic for this date. However, let's gather anyway, two discussion topics are suggested: (old) eeg story and an interesting essay paper by Lazebnik

 Can a biologist fix a radio? Cancer Cell. 2002 Sep;2(3):179-82. available with campus IP from, here is the link



As Michael suggested we will continue the study of eeg prediction/detection

The relevant materials are availalbe on Clinical Neurophysiology, Volume 116, Issue 3, Pages 489-741 (March 2005)


April 29

1pm, Science Building LD229 (Note unusual location due to make-up finals in the seminar room)

A new electrical brain stimulator in epilepsy

Speaker: Bob Worth, Neurosurgery and Mathematics, IUPUI

Bob will talk about clinical trials of a new anti-epileptic "on-demand" bran stimulator to control epilepsy We also will continue old discussion about dynamics of synchronization during seizures

(see an in vivo study Mormann F, Kreuz T, Andrzejak RG, David P, Lehnertz K, Elger CE. Epileptic seizures are preceded by a decrease in synchronization.Epilepsy Res. 2003 Mar;53(3):173-85. )


April 22

Reading club - we continue a discussion from the previous week (which was interrupted due to faculty foto:)


April 15

Reading club

Eugine Izhikevich book Dynamical Systems in Neuroscience Chapter 4

Bryan Melsheimer (Mathematics) is a moderator for this meeting You can download the book manuscript from Eugine's web page


April 8

1pm, Science Building LD027 (Note unusual location)

R. Andrew Chambers

(Director, Laboratory for Translational Neuroscience of Dual Diagnosis Disorders

Institute of Psychiatric Research, Indiana University School of Medicine)

Why we are Born Again in the Head: Computational Modeling of Hippocampal Neurogenesis

( go to Dr. Chamber's webpage and follow the links via Pubmed to neurophyscopharmacology to download the relevant paper)

March 18

Journal club

Robustness and parameter selection for conductance-based models

Leonid Rubchinsky

We will discuss the issues of robustness for HH-like models (Global structure, robustness, and modulation of neuronal models. Goldman MS, Golowasch J, Marder E, Abbott LF. J Neurosci. 2001 Jul 15;21(14):5229-38. Similar network activity from disparate circuit parameters. Prinz AA, Bucher D, Marder E. Nat Neurosci. 2004 Dec;7(12):1345-52.


March 11

Journal club

Scale-Free Brain Functional Networks. Phys. Rev. Lett. 94, 018102 (2005) by Eguíluz et al.


February 25

Reading club

Eugine Izhikevich book Dynamical Systems in Neuroscience Chapter 3 Dr. Worth (Neurosurgery and Mathematics) is a moderator for this meeting

You can download the book manuscript from Eugine's web page


February 15

10:40am, Engineering Building SL108

Alexey Kuznetsov

(Boston University)

Modeling of transient high-frequency firing in dopamine neuron: dynamical mechanisms and role of dendritic geometry

(Note unusual day of the week, time and location)


Mesencephalic dopamine neurons ordinarily will not fire faster than about 10/s in response to somatic current injections. However, in response to dendritic excitation, much higher rates are briefly attained. In an analysis of a simplified biophysical model, we suggest a way such high-frequency transient firing may be expected to occur in response to simultaneous dendritic and somatic stimulation. Our model represents the neuron as a number of electrically coupled compartments with different natural spiking frequencies, which correspond to the soma and parts of the dendrite. The primary hypothesis is that the soma is susceptible to loss of spiking due to inactivation of the Na channel, and that rapid activation of AHP currents in distal compartments is partly responsible for preventing this inactivation. We show that a difference in natural frequencies of the compartments is necessary for the transient oscillations to occur. That difference does not by itself ensure a significant difference between transient and steady state
frequencies, and we distinguish two dynamically different mechanisms contributing to the latter frequency difference. We show that a neuromodulation in the distal dendrites accompanying the release from
hyperpolarization in the soma is sufficient to elicit the high-frequency transient. For example, any neuromodulation that produces a decrease in the dendritic calcium conductance can elicit the high-frequency transient.



February 4

Journal club

Synchrony in gamma-range in perception: normal conditions vs. cognitive abnormalities (schizofrenia)

(Neural synchrony indexes disordered perception and cognition in schizophrenia, by KM Spencer et al., PNAS Dec 2004


January 28

The discussion will be continued


January 21

Discussion: use of scalp eeg signals for the control of movement

Speaker: Bob Worth, Neurosurgery and Mathematics, IUPUI

(see a recent paper by Walpaw and McFarland


January 14

We will continue Dec 17 discussion


WINTER BREAK - Happy holydays!



FALL 2004


December 17

Discussion of "Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks"

by Kopell and Ermentrout, PNAS, 101, 15482 (2004) (


November 19

Eye movements in  asymptomatic and recently diagnosed individuals with the genetic marker for Huntington’s disease

Speaker: Tanya Blekher, Ph.D.

(Director, Ocular Motility Laboratory; Research Professor,  Department of Ophthalmology, IU Medical School).


November 12

Journal Club

On the estimation of phase and phase synchronization

Speaker: Leonid Rubchinsky

The most popular definition of phase of non-periodic oscillations is "Hilbert phase". The phase defined in this way may lead to spurious phase synchronization in certain cases. I'll talk about modification of the definition of the phase (due to Eugene Izhikevich), which may avoid some of the problems with Hilber phase and phase synchronization detection.


November 5

"What was new at Neuroscience2004"


October 29

Departmental Colloquium "Modeling neuronal Dynamics" by J. Fox, U Colorado, LD229 3:30pm


October 15

Journal club

The brainweb: phase synchronization and large-scale integration. Varela F, Lachaux JP, Rodriguez E, Martinerie J. Nat Rev Neurosci. 2001 Apr;2(4):229-39.


October 8

Journal Club

New paper for discussion is

Theoretical Investigation of the Neuronal Na1 Channel SCN1A: Abnormal Gating and Epilepsy.  by Clancy and Kass, Biophys J 86:2606 (download here)

NOTE: October 8 colloquium at the Department of Mathematical Sciences may be of interest to seminar's participants

(LD 010, Avner Friedman, Ohio State University

Programs and Research Problems at the Mathematical Biosciences Institute)


September 24

Journal Club

We will discuss processing of natural scenes

(Kayser et atl. Curr Opin Neurobio 14:468, 2004


September 17

Journal Club

Synchronization in biologically-motivated models of networks

Speaker: Robert Worth (Dept of Neurology, IUSM and Dept Math Sci, IUPUI) (Bob will talk in parallel with Ermentrout's review of "Synch" by Strogatz, link


September 10

Journal Club

It there desynchronization of oscillations during epileptic seizures ?

Speaker: Leonid Rubchinsky, Dept Math Sci, IUPUI and Stark Institute, IUSM

(see also a paper: Theoden I. Netoff, and Steven J. Schiff. Decreased Neuronal Synchronization during Experimental Seizures. J. Neurosci. 22: 7297-7307)