docDynamic Instabilities in Neuroscience The Visions of Shamans:
download 
Report Transcription
Dynamic Instabilities in Neuroscience The Visions of Shamans:
The Visions of Shamans: Dynamic Instabilities in Neuroscience Bard Ermentrout October 2004 The Vision of Shamans – p.1/35 How does an animal switch gaits? Walk LH LF RH RF Trot LH RH RF LF Transverse Gallop LH−RH LF−RF The Vision of Shamans – p.2/35 What determines stripes or spots? The Vision of Shamans – p.3/35 How do fireflies sync? Single insect Bush 1 sec The Vision of Shamans – p.4/35 Dynamic Instabilities Transitions from one state to another governed by nonlinear equations Mathematics uncovers common features The Vision of Shamans – p.5/35 Dynamic Instabilities Transitions from one state to another governed by nonlinear equations Mathematics uncovers common features What are the basic principles for pattern formation? The Vision of Shamans – p.5/35 An Example Hallucinations & Entoptic Phenomena The Vision of Shamans – p.6/35 Cave art The Vision of Shamans – p.7/35 Meanings? What do the geometric signs in Upper Paleolithic Art mean? The Vision of Shamans – p.8/35 Meanings? What do the geometric signs in Upper Paleolithic Art mean? Compare to other modern cultures San (bushman) rock paintings Shoshonean Coso tribe Tukano tribes in Brazil Australian aboriginal tribes The Vision of Shamans – p.8/35 Hedges’ classification The Vision of Shamans – p.9/35 A Hypothesis Lewis-Williams, Hedges, and other anthropologists suggest nonrepresentational paleolithic art inspired by shamanic visions Psycho-active substances, eg datura (jimson weed), peyote, and yaje’ common in ceremonies with flickering fire, chanting leads to altered states The Vision of Shamans – p.10/35 Huichol shamanism Huichol rug designs inspired by visions Huichol yarn painting depicts the hunt for peyote The Vision of Shamans – p.11/35 Entoptic phenomena Visual images from within The Vision of Shamans – p.12/35 Entoptic phenomena Visual images from within Common in hallucinogenic drugs Premigrainous auras Flicker/pressure phosphenes The Vision of Shamans – p.12/35 Phosphenes The Vision of Shamans – p.13/35 Hildegard Premigrainous Auras? Hildegard of Bingen (1098 − 1179) The Vision of Shamans – p.14/35 The 60’s The Vision of Shamans – p.15/35 Form constants Spiral/vortex Funnel/tunnel Cobwebs/filigrees Exploding light rays Mosaics The Vision of Shamans – p.16/35 Retino-cortical transform a π/2 cortex log(e) −π/2 π/2 e a −π/2 retina (e, a) −→ ea λ log(1 + e/e0 ), −λ e0 + e The Vision of Shamans – p.17/35 Like the complex logarithm e exp(ia) → (log e, a) The Vision of Shamans – p.18/35 What are the patterns now? The Vision of Shamans – p.19/35 Recapitulating There are common patterns to shamanistic art The Vision of Shamans – p.20/35 Recapitulating There are common patterns to shamanistic art Transform to geometric patterns in cortex The Vision of Shamans – p.20/35 Recapitulating There are common patterns to shamanistic art Transform to geometric patterns in cortex How do these patterns arise? The Vision of Shamans – p.20/35 Inside the box computer fast camera Spontaneous activity shows spatial periodicity display Tsodyks et al Science 1999 Similar to evoked activity Visual system is poised near “instability” 2 mm The Vision of Shamans – p.21/35 The parts Pyramidal cell Basket cells The Vision of Shamans – p.22/35 Why doesn’t it always happen? Cortex is poised near instability Manipulation must push it past the point Drugs, flicker, pressure should be enough The Vision of Shamans – p.23/35 The local equations . . . E c ei cee I c ii c ie τe dE = _ E + Fe ( cee E _ cie I + Te ) dt decay rate change of activity τi dI dt output excitatory coupling inhibitory coupling sensory input = _ I + Fi ( cei E _ cii I + Ti ) The Vision of Shamans – p.24/35 . . . in a spatial array dEjk τe dt dIjk τi dt = −Ejk + Fe [ X Wee (j − j 0 , k − k 0 )Ej 0 ,k0 j 0 ,k0 − Wie (j − j 0 , k − k 0 )Ij 0 ,k0 + Te (t)] X = −Ijk + Fi [ Wei (j − j 0 , k − k 0 )Ej 0 ,k0 j 0 ,k0 − Wii (j − j 0 , k − k 0 )Ij 0 ,k0 + Ti (t)] The Vision of Shamans – p.25/35 Dynamic instability There is a constant equilibrium state This can be made unstable Translation and rotational symmetry forces the patterns The Vision of Shamans – p.26/35 The Underlying Mechanism _ 0 + + + 0 _ positive + _ space _ interaction strength Lateral Inhibition negative The Vision of Shamans – p.27/35 How this works Slight inhomogeneity and so on ..... leading to a final patterned state _ __ + ++ ++ __ _ is amplified by local excitation while surrounding region is depressed in turn, amplifying farther regions and depressing their neighbors The Vision of Shamans – p.28/35 Then what? Near the transition all dynamics is the same! Nonlinear analysis is needed Amplitude equations: E(x, y) ≈ r cos nx + s sin ny r 0 = r(p − ar 2 − bs2 ) s0 = s(p − as2 − br 2 ) a<b s = 0, r > 0 a<b r = 0, s > 0 a>b r > 0, s > 0 The Vision of Shamans – p.29/35 Drugs Mescaline, LSD, etc have common molecular mechanism Bind to special serotonin receptors in brain Increase in glutamate production =⇒ greater excitation Blocked by 5HT2A antagonists High occurrence of 5HT2A in schizophrenia The Vision of Shamans – p.30/35 Pressure phosphenes I dE/dt=0 dI/dt=0 E Reduce background activity Pressure on optic nerve suppression of inputs - like sensory deprivation Paradoxical excitation The Vision of Shamans – p.31/35 LSD Flight simulator The Vision of Shamans – p.32/35 Flicker instability Lateral Inhibitory Network P/2 Spatially uniform periodic input with double the natural frequency P Each cell has periodically damped impulse response time Simulation The Vision of Shamans – p.33/35 Other examples Transition from rest to oscillation The Vision of Shamans – p.34/35 Other examples Transition from rest to oscillation Transition from asynchrony to synchrony (temporal patterns) The Vision of Shamans – p.34/35 Other examples Transition from rest to oscillation Transition from asynchrony to synchrony (temporal patterns) Spots vs Stripes The Vision of Shamans – p.34/35 Conclusions Dynamic instabilities underly many natural patterns The Vision of Shamans – p.35/35 Conclusions Dynamic instabilities underly many natural patterns Idea of “lateral inhibition” is very generic The Vision of Shamans – p.35/35 Conclusions Dynamic instabilities underly many natural patterns Idea of “lateral inhibition” is very generic Local dynamics looks the same under the microscope The Vision of Shamans – p.35/35
