two wings:(di-ptera)neuralsuperpositioneyeshind winggyroscopes(halteres)specialized“power”musclesACTUATORSSENSORSCOMPUTER~500,000 neuronsReview from last Dickinson lecture……Control Theory Approaches to Biological SensorsSensory systems of interest to students of control theory because:1) Sensory cells dominate most nervous systems.motorsensoryinterneurons24,000242) Animals make great sensors.eg. insect eyes operates over8orders of magnitudes, compared to a “good” 12 bit CCDSilk moth malecan detect single molecule.in flyflight system:3) Sensory process extremely amenable to control theory.uH(s)we can treat sensory system as transfer function:energyneuralcode(input)(output)sensorysystemyy = H(s) u, where H(s) is transfer function.Sensory neurons transform energy in the external world into neuronal output.3) Sensory process extremely amenable to control theory:uH(s)we can treat sensory system as transfer function:energy neural code(input)(output)sensorysystemyy = H(s) u, where H(s) is transfer function.Sensory neurons transform energy in the external world into neuronal output.Consider ‘basic’ neuron….dendrites(input)cell body(nutritive)axon(transmission)“spike train”terminals(output)• neuron receives chemical transmitter from pre-synaptic cell • synaptic input alters DC potential in dendrties• DC potential in dendrites alters spike rate in axon• spike rate alters release of chemical transmitter in terminals• transmitter alters DC potential of post-synaptic cellBasic Neural Information Flowsensory process broken into three steps:1) Coupling2) Transduction3) EncodingC T Einputoutputcoupling transduction encodingenergy in external worldenergy at dendriteenergy at dendritetrans-membrane potentialtrans-membrane potentialspike ratelinear cascade of 3 transfer functionsinsect ‘hair’ cellsConsider sensory neuron….Coupling is performed by non-neuronal accessory structures, e.g. vertebrate inner ear…..1. Couplingear ossiclesmatch air-to-waterimpedancecochleaFourierdecompositionbasilarmembranefrequency response varies base-to-tip:Coupling,cont.One at dendrite, energy must activate ion channel to change current flow across membrane….2. TransductionIn general, 2 kinds of transduction processes:+direct:+2ndmessenger mediated:ABadvantage: fastadvantage: high gainamplification possibleSpike encoding is need for long distance transmission3. Encoding ABABtonic responsephasic responseProblem with encoding is limited dynamic range.stimulusintensityspikerate500 Hz ceiling several log stepsstimulusintensityspikeratemax. sensitivity= rangefractionationHow do neurons actually encode information?Encoding, cont…1) rate codestimulusspikesspikeratemagnitude of stimulus encodedby spike frequency1) temporal codestimulusspikescode00000100100000110000010100000010000010100010010temporal features of simulus encodes by precise position of spikesWho/what decides whether a cell is using a rate code vs. a temporal code?How do we characterize sensory cells? – or any ‘unknown system for that matter?Systems Indentificationemploy “Systems Indentification”:input ????ouputinstead of designing a transfer function, simply measure it:phasegainfrequencycreate Bode Plotfor unknown systemstimulusspikesspikeratein practice cells respond like this:responseis “clipped”H(s)linear filter static rectifierThis cascade describes many sensory cells.H(s) = ms2+ bs + k 1fit measured response to particular model, e.g.solve for m,b,k via least squaresSystems ID leads to interesting trick with sensory cells….Identification methods using noise….Sine wave analysis takes time, a shortcut is to use noise:input ????output‘white’ noise contains all frequencies with gaussian amplitudesHow do you extract H(s)? If input, u(t) is noise, then system, h(t) may be found by:τττdtutyPTh )()(1)(0∫∞−== cross correlationof input and outputIf input, output, y(t) is spike train, such that y(t) = 1 during spike, 0 elsewhere, then:τττ∆−=∑=KktuPTh1)(1)(= signal average of inputpreceding each spike!thus, system equals input “most likely to succeed”= reverse correlation techniqueNoise Approach Exampleaverage = h(s)FourierTransformBode plots for different
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