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Stochastic Resonance in Thalamic Neurons and Resonant Neuron Models

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Stochastic Resonance in Thalamic Neurons and Resonant Neuron Models STOCHASTIC RESONANCE IN THALAMIC NEURONS AND RESONANT NEURON MODELS by STEFAN REINKER Diplom-Mathematiker, Westf¨alische Wilhelms-Universit¨atM¨unster, 1997 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Mathematics Institute of Applied Mathematics We accept this thesis as conforming to the required standard ..................................... ..................................... ..................................... ..................................... ..................................... THE UNIVERSITY OF BRITISH COLUMBIA January 2004 c Stefan Reinker, 2004 Abstract Neurons of the thalamus are major participants in gating sensory information for relay to the neocortex. Thalamic neurons are crucially involved in rhythmogenesis which determines the sleep/wake cycle. These roles require critical involvement of a T-type calcium current, conferring a frequency preference in response to subthreshold signals. We examine the interactions of this membrane resonance and noise using whole-cell patch clamp recordings in thalamocortical and reticular neurons of rat brain slices. We perform Monte-Carlo simulations and mathematical analysis using Hodgkin-Huxley-type and polynomial models of resonant neurons. We demonstrate stochastic resonance (SR) as maximal coherence between the input and stochastic output at intermediate noise levels. SR is measured by determining the signal-to-noise ratio under sine wave inputs, and from the reliability of detection measure under α-function inputs. In the experiments and neuron models with T-current, we demonstrate subthreshold resonance at 2-3 Hz, as well as noise dependent frequency dependence of SR for sine wave inputs. The simpler Hindmarsh-Rose model has a similar SR. This model also shows improved detection when the delay of consecutive EPSPs matches the preferred frequency. We show that the preferred frequency of the subthreshold and stochastic resonances depends on the time scale of the slow variable. The stochastic frequency preference arises from modulation of the firing probability of the fast subsystem. We develop a simple linear integrate-and-fire model with subthreshold resonance, which retains the main features of the more complicated models. An analytical solution of the stochastic equations shows that the eigenvalues determine frequency preferences in subthreshold resonance and stochastic resonance. SR can occur even with only noise. This autonomous SR depends on the resonance in our experiments and models. We demonstrate that preferred stochastic firing in the single neuron model translates into syn- chronized behaviour in a noisy network of resonant neuron models. With inhibitory synaptic coupling, noise can extend the parameter range of oscillations. With excitatory synaptic cou- pling, noise produces synchronized oscillations of the quiescent deterministic network. We speculate that combined subthreshold membrane resonance and stochastic resonance have physiological utility in coupling synaptic activity to preferred firing frequency, and in network synchronization under noise. ii Table of Contents Abstract ii Table of Contents iii List of Figures vi Acknowledgements and Dedication ix Chapter 1. Introduction 1 1.1 Stochastic resonance ............................................................. 2 1.1.1 SR in experiments ........................................................ 3 1.1.2 SR in models of neurons .................................................. 4 1.2 Physiology of thalamic neurons .................................................. 5 1.3 Noise and information processing in neurons ..................................... 7 1.4 Neuronal networks ............................................................. 10 1.5 Aims, scope, and organization .................................................. 12 Chapter 2. Methods 15 2.1 Experimental methods .......................................................... 15 2.1.1 Slice preparation ......................................................... 15 2.1.2 Recording procedures .................................................... 15 2.1.3 Input signals ............................................................. 17 2.2 Measures of stochastic resonance ................................................ 18 2.2.1 Signal-to-noise ratio with interspike interval histograms ................... 18 2.2.2 α-function stimulation ................................................... 21 2.3 Numerical methods ............................................................. 23 Chapter 3. Experiments 25 3.1 Introduction .................................................................... 25 3.2 Thalamocortical neurons ....................................................... 26 3.2.1 ZAP function stimulation ................................................ 26 3.2.2 Sine wave stimulation with noise ......................................... 26 2+ 3.2.3 Blockade of IT with Ni ................................................ 32 3.2.4 α-function stimulation ................................................... 33 3.2.5 Noise stimulation with no signal .......................................... 35 3.3 Reticular neurons of the thalamus .............................................. 35 3.3.1 ZAP function stimulation in reticular neurons ............................ 38 3.3.2 Noise stimulation in reticular neurons .................................... 38 3.4 Discussion ...................................................................... 38 Chapter 4. Ionic Models of Thalamic Neurons 43 4.1 Introduction .................................................................... 43 4.2 Impedance analysis ............................................................. 44 iii Table of Contents 4.3 Stochastic resonance ............................................................ 46 4.4 α-function stimulation .......................................................... 49 4.5 Noise stimulation with no signal ................................................ 51 4.6 Reticular neurons .............................................................. 52 4.7 Discussion ...................................................................... 55 Chapter 5. The Hindmarsh-Rose model 59 5.1 Introduction .................................................................... 59 5.2 Bifurcation analysis ............................................................ 60 5.3 Subthreshold resonance ......................................................... 62 5.4 Noisy sine wave stimulation .................................................... 65 5.5 SR with α-function stimulation ................................................. 67 5.6 Noise stimulation with no signal ................................................ 69 5.7 Stochastic resonance in the fast subsystem ...................................... 70 5.8 Stochastic bifurcation analysis .................................................. 77 5.9 Discussion ...................................................................... 80 Chapter 6. The Resonant Integrate-and-Fire Model 82 6.1 Introduction .................................................................... 82 6.2 Matching the model and parameter estimation .................................. 83 6.2.1 Subthreshold properties .................................................. 83 6.2.2 Threshold properties ..................................................... 86 6.3 Stochastic resonance in the RIF model .......................................... 88 6.4 Comparison with the non-resonant integrate-and-fire model ..................... 89 6.5 Stochastic analysis of RIF ...................................................... 93 6.6 First passage time ............................................................. 101 6.7 Discussion .................................................................... 103 Chapter 7. Network Synchronization 104 7.1 Introduction .................................................................. 104 7.2 A network of Huguenard-McCormick neurons .................................. 105 7.3 A network of nRT neurons with inhibitory coupling ............................................................ 109 7.4 Physiological network of TC and reticular neurons ............................. 113 7.5 Hindmarsh-Rose network ...................................................... 116 7.6 Resonant integrate-and-fire neuron network .................................... 120 7.7 Discussion .................................................................... 124 Chapter 8. Conclusion 126 8.1 Summary of results ............................................................ 126 8.2 Relevance and implications .................................................... 129 8.3 Problems and future research .................................................. 131 Glossary 134 Bibliography 135 iv Table of Contents Appendix A. Model Parameters 149 A.1 Huguenard-McCormick model (HM) ........................................... 149 A.2 The model of reticular neurons of the thalamus (RET) ......................... 150 A.3 Hindmarsh-Rose model (HR) .................................................. 151 A.4 Integrate-and-fire models ...................................................... 151 A.5 Synaptic coupling ............................................................. 152 v List of Figures 2.1 DIC-IR videomicroscopy in-slice image of a MGB neuron during whole-cell patch clamp recording. ..........................................................................
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