I will present some of the methods I developed during my PhD-work for the study of stochastic resonance in leaky integrate-and-fire neurons. Specifically, I will present Markov-chain based methods for the calculation of the power spectral density of spike trains evoked by sinusoidal stimuli. Based on these methods, I will investigate the influence of signal frequency and background noise on the signal-to-noise ratio of the neuronal response, and discuss some scaling properties.
If anyone had an idea on how to prove that the interspike-interval density of the leaky integrate-and-fire neuron driven by sinusoidal input and Gaussian white noise is strictly positive for t>0 (except possibly at isolated points), I'd be very happy about suggestions. The proof in Section 2.2.3 of my thesis is, unfortunately, badly flawed.
Microbial fermentations, no matter whether they take place in "defined'' growth media or out in nature, occur in complex dynamic environments. The purpose of this talk will be to discuss a predictive modeling approach which handles this complexity while maintaining a mathematically tractable modeling framework. During this talk, the semi-mechanistic approach will be introduced by a few examples. Some basic fermentation microbiology will be provided and the approach will be applied to the study of acid tolerance in lactic acid bacteria growing in a complex medium. The work presented here may have application to other areas of research where dynamic alterations in chemical buffering are important.
The Collective Dynamics in Networks of Simple Neurons
Ion channels and receptors in the cell membranes and internal membranes are often distributed in discrete clusters. One particularly well studied example is the distribution of inositol 1,4,5-triphosphate receptors in the plasma membrane that controls the flux of Ca2+ from the endoplasmic reticulum into the cytosol. By using mathematical modeling, we show that channel clustering can enhance the cell's Ca2+ signaling capability.
Furthermore, we predict optimal signaling cellular capability at cluster sizes and distances that agree with experimentally found values in Xenopus oocyte.
Results of clinical research show strong connections between appearance of deep invaginations of the trophoblast tissue and pregnancy complications. Because the trophoblast tissue grows only by cell proliferation and fusion, it is important to analyse how the initiation of these processes can cause the tissue to bend. In my talk, I will show how the trophoblast tissue can be modeled using the immersed boundary method and will present simulations of tissue development, along with comparisons with clinically obtained results.
Reaction-diffusion systems, complex biochemical reaction chains, population dynamics, and many more natural phenomena are stochastic processes in which many different events can occur at any time. The simulation of such systems is a formidable task, and I will present some algorithms that allow for the efficient simulation of large systems of stochastic processes.
Briefly, the idea is to use Gillespie's algorithm to determine the time interval between any two events, and then use logarithmic classification of possible events to determine efficiently which event occurs at any one time step. Utilizing proper data structures, this classification and selection scheme can be implemented in a highly time-efficient manner (Fricke and Wendt, 1995).
I will give an introduction into the ideas underlying the logarithmic classification algorithm and give a brief tutorial on how to use the logarithmic class library in simulation code.
Preprint versions of papers explaining the algorithms, source code implementing logarithmic and discrete classes, and a sample program simulating a Lotka-Volterra-style model, is available as the Markov Classes Package
We develop minimal computational models to investigate how intrinsic cellular mechanisms can modify responses to dynamic sounds. Our models are based on experimental data, recorded from phase-disparity-sensitive neurons in auditory midbrain. I will talk about the experimental background of this work, describe our models, and show the results and their connection with experimental work.
Relaxation oscillations (RO), a highly nonlinear type of oscillation, are found in many biological, chemical, physical and neuronal problems. The characteristic feature of RO is a repeated switching between fast and slow motions. We will study the well known forced van der Pol oscillator, a model for a triode circuit. This oscillator exhibits all kinds of dynamical behaviour from synchronization up to 'chaos'. We will explain some of these properties by using techniques from dynamical systems, especially geometric singular perturbation theory (GSPT).
Stochastic Resonance (SR) is a phenomenon observed in nonlinear systems whereby the introduction of noise enhances the detection of a subthreshold signal for a certain range of noise intensity. SR has been observed in many physical and mathematical systems. The nonlinear threshold detection mechanism that neurons employ and the noisy environment in which they reside make it likely that SR plays a role in neural signal detection. While the role of SR in sensory neural systems has been studied, its function in central neurons is unknown. In many central neurons, such as the hippocampal CA1 cell, very large dendritic trees are responsible for detecting neural input in a noisy environment. Attenuation due to the electrotonic length of these trees is significant, suggesting that a method other than passive summation is necessary if signals at the distal ends of the tree are to be detected. The hypothesis that SR is involved in the detection of distal synaptic inputs was first tested in a computer simulation of a CA1 cell and then verified with in vitro rat hippocampal slices. The results strongly showed that SR can enhance signal detection in CA1 hippocampal cells. High levels of noise were found to equalize detection of synaptic signals received at varying positions on the dendritic tree. The amount of noise needed to evoke the effect is comparable with physiological noise in slices and in vivo. Computer simulations show that the phenomenon is enhanced in neuronal networks. Therefore both computer simulations and experiments suggest an important role for stochastic resonance in neuronal signal processing.
The olfactory system must be able represent a highly variable stimulus in such a way that an animal may recognize similar stimuli and discriminate among dissimilar ones. How an animal generalizes from its experience of an odor mixture to a new experience with another odor mixture may depend on the perceptual similarity of the mixtures. I will discuss behavioral and physiological evidence for odor coding in the olfactory system of insects. I will also discuss my research plans for my time as a postdoc at the MBI.
I describe a model of feedback from the primary visual cortex to the lateral geniculate nucleus, and use it to study the sensitivity to orientation discontinuity of lateral geniculate relay cells. I compare with experimental results and make a number of testable predictions.
Adrenal Zona Fasciculata (AZF) cells in the adrenal cortex secrete cortisol in response to ACTH, a hormone released by the pituitary gland. ACTH acts by depolarizing these cells leading to Ca+2 influx through T-type Ca+2 channels, which subsequently causes Ca+2 dependent cortisol release. Our laboratory has discovered an ATP activated, non-inactivating background K+ channel (Iac/TREK-1/KCNK2) in bovine AZF cells that serves to set the resting membrane potential of the cell (Mlinar et al, 1993; Enyeart et al, 1997). ACTH inhibits this channel at physiological concentrations leading to membrane depolarization (Mlinar et al, 1993). Thus our laboratory has identified the link between ACTH and cortisol secretion. In my talk I will discuss some of the important properties of this channel such as nucleotide dependence, agonists and antagonists and its cloning (Xu and Enyeart, 2001; Enyeart et al, 2002.). I will also briefly talk about some of the electrophysiological techniques that I have used in my work such as whole cell and single channel patch clamp recordings. Finally I would mention our idea of modeling the ionic currents in the bovine AZF cells to generate a model that would identify possible membrane potential oscillations and help determine the voltage dependent entry of Ca+2 into the cell necessary for optimal release of cortisol.
Mlinar B, Biagi BA, Enyeart JJ. A novel K+ current inhibited by adrenocorticotropic hormone and angiotensin II in adrenal cortical cells. J Biol Chem. 1993 Apr 25; 268(12): 8640-4.
Enyeart JJ, Gomora JC, Xu L, Enyeart JA. Adenosine triphosphate activates a non-inactivating K+ current in adrenal cortical cells through nonhydrolytic binding. J Gen Physiol. 1997 Dec; 110(6): 679-92.
Xu, L and Enyeart JA. Properties of ATP-dependent K+ channels in adrenocortical cells. Am J Physiol Cell Physiol. 2001 Jan; 280(1): C199-215.
Enyeart JJ, Xu L, Danthi S, Enyeart JA. An ACTH- and ATP-regulated background K+ channel in adrenocortical cells is TREK-1. J Biol Chem. 2002 Oct 3.
Odor discrimination in the rat: The role of spatial activity patterns in the olfactory bulb
Deep brain stimulation (DBS) represents a dramatically effective treatment for clinically intractable movement disorders such as essential tremor and Parkinson's disease; however the underlying mechanisms of its therapeutic action are unknown. The goal of my research program is to develop a systems level understanding of the effects DBS using detailed computer modeling techniques. My work couples the results of functional imaging and basic neurophysiology to computer models of extracellular electric fields and their effects on the nervous system. These models consist of three basic stages. The first step is the development of 3D finite element models of the electric field generated by DBS electrodes where the electrical properties of the tissue are based on diffusion tensor MRI. The second step is coupling the electric field to 3D reconstructions of neurons surrounding the electrode where the ion channel biophysics of the neuron models are based on experimental data. The outcome of steps 1 & 2 are predictions on the volume of tissue surrounding the electrode that are affected by the stimulation. The final step is then to apply those stimulation effects to large scale neuronal network models of the thalamo-cortical-basal ganglia system that DBS modulates thereby providing experimentally testable hypotheses on the effects of stimulation in the different nuclei of the network. In addition, the results of this work can be coupled to PET/fMRI to provide a contiunum from the single cell to the network to the behavior.
Noise or fluctuations has traditionally been regarded as a nuisance, interfering with the signal or information processing, and so efforts have been made to minimize the noise. The recent discovery of the noise-induced activation or ordering shows that under certain circumstances, noise can in fact dramatically help the performance or processing in systems.. Two of the common types of noise-activated processes are delineated, namely stochastic resonance and stochastic transition (noise-induced transition). Research on this paradoxical phenomenon and its applications has become virtually an paradigm-setter in the mathematics, physics and neuroscience.
We develop an algorithm for analysing perturbation-induced stability-instability properties of systems and such a technique may be used to actuate a noise-induced activation in various biological/clinical systems. Stochastic enhancement in neural, immunological, chemical and radiological processes is shown. We describe the mathematical analysis and experimental findings of such activation in biological/neural processes and elucidate applications towards diagnosis and therapy, in neurology, radiology and oncology, with special applications for management to brain lesions. The associated phenomenon of non-equilibrial de-stabilization of a pathological system under artificially engineered perturbation, is analysed in terms of Prigogine-Glansdorff Stability Theorem and we explore a computational model of fluctuational transitions in complex systems in general.
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- Collins, J, Gregg, P. (1997). Noise-mediated enhancements and decrements in human sensation, Phys Rev E, 56, 923-26.
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- Roy, P, Kozma, R, et al (2002). >From Neurocomputation to Immunocomputation: A method and algorithm for fluctuation-induced instability in biological systems, IEEE Trans. Evolutionary Computing, 6(3), 1-14, 2002.
- Roy, P. et al (2000). Tumour Stability Analysis, Kybernetes: Intl J of Systems Science, 29, 896-926.
- Simonotto, E, et al, (1997). Visual perception of stochastic resonance, Phys Rev Lett 78:1186-88.
Intra-parenchymal (i.e. directly into tissue) injection and transport of drugs and other agents to treat tumors and neurodegenerative diseases are being studied both theoretically and experimentally. The talk is divided into three parts. In the first, we discuss the phenomena that occur, and how to observe them principally via magnetic resonance imaging (MRI). In the second part, we review the status of the initial experiments we have undertaken in checking the predictions. Finally, we discuss how we model the phenomena, obtain the input parameters needed for the calculation, and solve the resulting equations.
Physical modeling in biomedical computing: a research agenda, Raghu Raghavan, Center for Information-enhanced Medicine (Ciemed) Internal Report, 22 pages, unpublished, July 1994, http://www.iemed.com/Aboutus/people/raghu/presentations/PM.pdf
A continuum-mechanical model for cortical growth, Raghu Raghavan, Wayne Lawton, S.R.Ranjan and R.R. Viswanathan, Journal of Theoretical Biology, Vol. 187, pp. 285-296, 1997
Form from growth: a mechanical model for cortical development and its control, R. Raghavan, W. Lawton, S.R.Ranjan and R.R Viswanathan, Ciemed Internal Report, 9 pages, unpublished, April 1997
Corticography, Jacobi fields, and symmetries. R. Raghavan
We describe the general setting for chemical reaction network theory based on mass-action kinetics. Recent methods are able to draw conclusions about the dynamics of the chemical composition, even in the absence of specific information about the reaction rate parameters. We present some of these methods and connections to cell and molecular biology.
Mitochondrial Modulation of Intracellular Ca2+ Signaling
The computation of shape change from physical principles, or morphodynamics, is an interesting problem in developmental biology. After a brief introduction, the talk will consist of three parts. In the first, a continuum model for the folding of brain cortical contours, in which growth is induced by a change in reference metric will be presented; with suitable constraints, this model gives rise to a variety of shapes akin to those actually seen. In the second part, the inverse (control) problem of estimating a time-dependent reference metric from initial and final data is used to match cortical contours, and is compared with an active contour method. Finally, the "symmetry" aspect of the growth will be discussed, and it is proposed that: a symmetry analysis of an equivalence class of models in the spirit of Sophus Lie may provide a useful taxonomy of such patterns, and that the domains of pseudogroups as the objects of symmetry breaking will be of interest in future mathematical developments. An integration of physics with biology in such fields will provide for a new discipline which we may call bioformatics.
Circadian rhythms of behavior and physiology are observed in a variety of organisms. In mammals, the suprachiasmatic nuclei (SCN) of the hypothalamus function as the major biological clock. The inherent pacemaker activity of the SCN can be effectively regulated by changes in the environmental light cycle. This allows an animal to synchronize its internal clock with the ever-changing light cycle encountered over a seasonal/yearly basis. What are the cellular events that allow light to affect clock timing? Recent work has revealed that coordinated transcriptional oscillations are required for circadian rhythm generation and that light-activated signaling events entrain the clock by resetting transcriptional rhythms. Given these observations, a characterization of the intracellular signaling pathways and downstream transcription factors activated by light will be critical for understanding the functional properties of the circadian clock. I will present data examining the role of the p42/p44 mitogen-activated protein kinase (MAPK) signal transduction pathway as a cellular signaling intermediate that couples light to circadian clock entrainment. If there is time left over, I will also present data looking at mechanisms of Ca2+-induced gene expression in cortical neurons.
This seminar is based on converging evidence from two very different experimental systems that involve glutamate as a neurotransmitter, and as an excitotoxic agent that kills neurons after injury.
Much of the excitatory synaptic transmission in the CNS is mediated by glutamate through post-synaptic receptors that open ion channels in response to glutamate release. Recent evidence suggests that changes in excitability at these synapses such as those that occur in long term depression (LTD) or potentiation (LTP) are due, in part, to rapid changes in the number of receptors located at the synapse due to modulation of receptor recycling.
Extracellular glutamate increases rapidly after injury to the CNS, and very high levels can cause neuronal and glial death by increasing intracellular Ca++ to toxic levels. Tumor necrosis factor-alpha (TNF) is an inflammatory cytokine that is released by immune cells and can induce necrotic and apoptotic death in target cells. After injury to the CNS, TNF levels increase markedly, and TNF has been thought to be a possible mediator of secondary cell death after stroke, spinal cord injury (SCI), and also in multiple sclerosis (MS). TNF also seems to increase glutamate actions in a brainstem circuit mediating gastric motility (Emch, Hermann, and Rogers, 2000). We tested the hypothesis that TNF and glutamate might interact after SCI by making nano-injections of TNF or the glutamate agonist kainic acid (KA) into the spinal cord gray matter either alone or together (Hermann et al, 2001). Low doses or either agent produced no cell death; together, they killed large numbers of neurons within 90 minutes. This potentiation of cell death was completely blocked by CNQX, which is an antagonist at AMPA-type glutamate receptors. This suggested that TNF might in some way be altering AMPA-R excitability.
To test this, we engaged the help of collaborators at Stanford and applied TNF to hippocampal neurons in culture (E. Beattie et al, 2002). 15 minutes after application of TNF, AMPARs on the surface of dendrites increased dramatically. Whole cell patch clamp showed a concomitant increase in spontaneous excitatory post-synaptic currents. Reduction of endogenous TNF by antibody treatment reduced AMPAR surface expression and epsc's. Experiments in hippocampal slice also showed a role for TNF in modulating synaptic activity. We showed that changes in extracellular K+ changed both AMPAR surface expression and susceptibility of cerebellar granule cells to excitotoxic cell death (Ha et al, 2002). Thus it appears that modulation of AMPARs by TNF (and other agents) may be involved in both synaptic plasticity (and learning?) and the induction of cell death. There are some therapeutic implications of these findings.
In this (informal) talk we will present a brief overview of cluster analysis, and discuss its application to the diagnosis of breast cancer using gene expression (micro) arrays. The talk will present some common clustering algorithms, and describe several statistical problems that arise in the application and interpretation of clustering methods.
In this research, we use methods from information processing to constrain neural models in an attempt to capture not only the dynamics of a system but also its computational function. We study the cricket cercal sensory system, a model system that mediates the detection and analysis of low velocity air currents. The input to the system is represented in an afferent map which encodes sensory stimuli in spatiotemporal patterns of activity. We are able to predict the dynamic patterns of activity that emerge from the ensemble in response to different stimuli. We use these predicted activity patterns to study how interneurons extract sensory information at the next layer of processing. Our main goal is to determine the biophysical mechanisms that implement the encoding schemes in this sensory system.
The cerebellum is a region of the central nervous system responsible for the coordination of complex motor movements. It consists of bilaterally symmetrical nuclei surrounded by a highly convoluted cortex. Numerous anatomical, physiological and biochemical studies have resulted in a detailed description of its cellular and molecular components, circuitry and sequence of developmental events. Nevertheless, despite the wealth of descriptive data, our understanding of the rules and relationships leading to the formation of the cerebellum and to the acquisition of its functional properties is lagging behind. In this presentation the current state of our knowledge concerning the cerebellum will be outlined and potential opportunities for mathematical modeling will be suggested.
Oscillatory Neural Networks (ONN) will be described and compared with other NN paradigms. ONN models of attention and novelty detection will be presented. These models are based on principle of synchronization of neural activity which is a very powerful principle of computational neuroscience.
Taste buds are collections of 50 to 100 individual taste receptor cells (TRCs). These cells detect the presence of chemical stimuli within the oral cavity and relay this information to the central nervous system via synaptic connections with afferent nerve fibers. The "historical" view of this process describes a single TRC as becoming depolarized when stimulated by tastants by elusive transduction mechanisms and subsequently releasing transmitter onto the afferent nerve. Many TRCs were known not to synapse with the afferent nerve fibers and were believed to be supporting cells. Recent developments in the physiology and molecular biology of TRCs have made it clear that this view is no longer tenable. Classes of recently cloned taste receptor molecules for bitter and sweet stimuli and related transduction enzymes have been localized to TRCs that lack synapses to the afferent nerve. How then do these cells, which possess the machinery to respond to taste stimuli, relay this information to the central nervous system? Our laboratory has discovered several signaling pathways endogenous to the taste bud that can serve as mechanisms for cell to cell communication among the TRCs of the bud. These include classic neurotransmitters, such as norepinephrine and serotonin, and neuropeptides, such as cholecystokinin. For the most part, it appears that certain subsets of TRCs express a signaling agent while other subsets of TRCs express a receptor for this agent. As well, physiological responses can be measured to exogenous application of these agents. Thus these pathways may serve unrecognized manners of information processing and modulation of the gustatory signal prior to afferent nerve stimulation.
The cortical surface of the human brain is a highly folded, convoluted structure that is 3-5 mm thick and topologically equivalent to a sheet. Most of the functional processing of the brain occurs on this sheet. However, the folding patterns vary considerably between individuals in terms of the shape, depth, length and location of the folds. As a result, neuroscientists are interested in 2D analysis methods and tools for comparing function and anatomy across subjects which can take into account some of this individual variability.
I am using methods from complex analysis, computational geometry, topology and image processing to "unfold" and "flatten" the cortical surface of the brain. While it is impossible to create areal or length preserving maps of a highly convoluted surface such as the brain, the Riemann Mapping Theorem describes the existence of conformal maps. I will discuss methods and theory from the area of "circle packings" which I am using to create approximations to discrete conformal maps of the brain. I will discuss some of the computational and topological issues that arise and how I am imposing coordinate systems on these maps. I will show some of the brain maps that I have created and discuss collaboration results with neuroscientists who are interested in depression, schizophrenia and Alzheimer's diseases.
Tumor suppressor function during development and tumorigenesis
Oscillatory neural model (ONM) with traditional Hebbian-like learning rule for associative memorization of sequences is considered
ONM of novelty detection which is based on frequency encoding of input information and oscillatory mechanism of memory formation will be presented. The adaptation of natural frequencies of network oscillators to the frequency of the input signal is used as the mechanism of information memorization. The recognition principle for familiar stimuli is based on the resonance amplification of network activity
A new ONM that combines consecutive selection of objects, attention focus formation, memorisation, and discrimination between new and familiar objects has been developed. The model works with visual information and fulfils the following operations: (1) separation of different objects according to their spatial connectivity; (2) consecutive selection of objects located in the visual field into the attention focus; (3) representation of objects in the working memory; and (4) novelty detection of objects.
Adrenocortical cells secrete corticosteroids in response to ACTH released from the pituitary. Although adrenocortical cells lack Na+-dependent action potentials, the hallmark of excitable cells, cortisol secretion depends on depolarization-dependent Ca2+ entry through voltage-gated Ca2+ channels. A model is presented for cortisol secretion which depends on the three specific ion channels present in these cells. The model proposes a novel role for T-type Ca2+ channels.