Lecture 1: Neurons. Lecture 2: Coding with spikes. To gain a basic understanding of spike based neural codes

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1 Lecture : Neurons Lecture 2: Coding with spikes Learning objectives: To gain a basic understanding of spike based neural codes

2 McCulloch Pitts Neuron I w in Σ out Θ Examples: I = ; θ =.5; w=. - in = *. <.5 x= I = ; θ =.5; w = 2. in = *2. >.5 x =

3 Exercise: Use networks of McCulloch Pitts neurons to create a NOT, AND, OR and XOR device. Connections or synaptic weights between neurons can be positive or negative. Define threshold and synaptic weights and assume that a neuron s output can be either or. in NOT out in AND in2 out in OR in2 out in XOR in2 out in out In in2 out In in2 out In in2 out NOT w= - I Σ out Θ=-.5 I in - out in = w*i = -.*I

4 Exercise: Use networks of McCulloch Pitts neurons to create a NOT, AND, OR and XOR device. Connections or synaptic weights between neurons can be positive or negative. Define threshold and synaptic weights and assume that a neuron s output can be either or. in NOT out in AND in2 out in OR in2 out in XOR in2 out in out In in2 out In in2 out In in2 out AND I I2 w= w2= Σ out Θ>=.5 I I2 in out 2 in = w*i+w2*i2 =.*I+.*I2

5 Exercise: Use networks of McCulloch Pitts neurons to create a NOT, AND, OR and XOR device. Connections or synaptic weights between neurons can be positive or negative. Define threshold and synaptic weights and assume that a neuron s output can be either or. in NOT out in AND in2 out in OR in2 out in XOR in2 out in out In in2 out In in2 out In in2 out OR w= w= Σ out Θ>=.5 I I2 in out 2 in = w*i+w2*i2 =.*I+.*I2

6 Exercise: Use networks of McCulloch Pitts neurons to create a NOT, AND, OR and XOR device. Connections or synaptic weights between neurons can be positive or negative. Define threshold and synaptic weights and assume that a neuron s output can be either or. in NOT out in AND in2 out in OR in2 out in XOR in2 out in out In in2 out In in2 out In in2 out XOR NOT AND OR I I2 I w= w= w= Σ Σ w= I2 In Θ>=.5 Θ>=.5 out w= w=- out2 Σ In2 out out2 In3 out3 Θ>=.5 out3 w=- w= I Σ out Σ I in Θ=-.5 out I I2 - I I2 w2= Θ>=.5 in out out w= w= I Σ I2 Θ>=.5 in out out in = w*i = -.*I 2 2 in = w*i+w2*i2 =.*I+.*I2 in = w*i+w2*i2 =.*I+.*I2 2 2

7 v(t) x(t)=f(v(t),θ).. Output x(t) = F(v(t), θ). I(t)=Σi i (t).. Total input dv/dt = ci(t) x v Θ I Θ v(t) time v(t) x(t)=f(v(t),θ).. Output I(t)=Σi i (t).. Total input γ x(t) = F(v(t), θ) x(t). v(t) Θ v(t) I(t)

8 Exercise: (a) You want to create a sensory neuron that responds to sensory stimuli ABOVE a certain threshold with a close to linear input-output function. The response should be in spikes/second. You can assume that the input changes on a very slow time scale (minutes). Choose one of the three types of neurons above to implement this sensory neuron and defend your choices. (b) You want to create a sensory neuron that responds to ANY sensory input and has a linear input-output function. The response should be expressed in spikes/seconds. You can assume that the input changes on a very slow time scale (minutes). Choose one of the three types of neurons above to implement this sensory neuron and defend your choices. a) b)

9 v(t) x(t)=f(v(t),θ).. Output x(t) = F(v(t), θ). Θ I(t)=Σi i (t).. Total input dv/dt = ci(t) x v Θ I v(t) time a) v(t) x(t)=f(v(t),θ).. Output? x(t) = F(v(t), θ). I(t)=Σi i (t).. Total input γ x(t) v(t) Θ v(t) I(t) b)

10 I I2 I3 w w2 v(t) w3 in w2 x v(t) in2 x in = w*i+w2*i2+w3*i3 v = F(in, τ) x=f(v, θ) in2 = w*x v2 = F(in2, τ) x2=f(v2, θ)

11 Exercise: You have three McCulloch Pitts neurons. All three have the possible states and, and their thresholds are.. Two neurons receive outside inputs (in, in2), and these two make synapses with the third who is considered the output (o). You want the output to be when the sum of the inputs > 4, otherwise. How do you choose your synaptic weights?

12 Lecture 2: Can a Neural Code be Defined? Neural code? We (neuroscientists) place ourselves in the position of the homunculus, monitoring neural activity in the brain as stimuli vary in time along an unknown trajectory.

13 Can a Neural Code be Defined? Lecture 2: Can a Neural Code be Defined? Neurons signal information in a various manners. For the time being, we will restrict our discussion to information signaling via Spikes, or Action Potentials. Lord Adrian's discoveries (92ies): () Individual Neurons produce stereotyped action potentials. (All-or-none law)

14 In the simplest case, the number of action potentials fired would correlate directly with the amplitude of the applied stimulus. Lecture 2: Can a Neural Code be Defined? Number of action potentials Amplitude "Rate" or "# of action potentials" measured over window of stimulus application "Amplitude - to - frequency transformation" or "rate coding" Lord Adrian's discoveries (92ies): (2) In response to a static stimulus, the rate of spiking increases as the stimulus becomes larger.

15 Lecture 2: Can a Neural Code be Defined? Example: s of olfactory receptor neurons to odor stimuli of increasing concentration.

16 Example: s of cold receptors to progressively colder stimuli Lecture 2: Can a Neural Code be Defined?

17 What's wrong with this picture? Lecture 2: Can a Neural Code be Defined? Number of action potentials Amplitude () Neurons don't fire at arbitrarily high frequencies Number of action potentials Saturation Amplitude

18 Lecture 2: Can a Neural Code be Defined? (2) Neurons don't always fire in response to arbitrarily low stimulus amplitudes Number of action potentials Saturation Amplitude Threshold

19 Lecture 2: Can a Neural Code be Defined? Lord Adrian's discoveries (92ies): (2) If stimulus is continued for a long time, spike rate begins to decline (adaptation).

20 Lecture 2: Can a Neural Code be Defined? Number of action potentials Saturation This "static" representation of a neuron's response curve is rarely accurate because most neurons exhibit some form of adaptation, desensitization or habituation. Amplitude Threshold

21 Lecture 2: Can a Neural Code be Defined? Rate code? Number of action potentials Amplitude "Rate" measured over window of stimulus application Action potential frequency Amplitude

22 Lecture 2: Can a Neural Code be Defined? Rate code? Number of action potentials Amplitude "Rate" measured over window of stimulus application Action potential frequency Amplitude

23 Rate code? Number of action potentials Action potential frequency Lecture 2: Can a Neural Code be Defined? Amplitude Amplitude "Rate" measured over window of stimulus application First interspike interval Amplitude

24 "Rate" depends strongly on definition and method Lecture 2: Can a Neural Code be Defined?

25 Temporal code? Amplitude Amplitude Amplitude First interspike interval Action potential frequency Number of action potentials Amplitude Lecture 2: Can a Neural Code be Defined? Latency to first spike

26 Lecture 2: Can a Neural Code be Defined? Temporal code? # of occurrences 3 2 Interspike intervals # of occurrences 3 2 Interspike intervals amplitude is defined by distribution of interspike intervals # of occurrences 3 2 Interspike intervals

27 Lecture 2: Can a Neural Code be Defined? Temporal code? # of occurrences 3 2 Interspike intervals # of occurrences 3 2 Interspike intervals amplitude is NOT defined by distribution of interspike intervals # of occurrences 3 2 Interspike intervals

28 Exercise: Write an equation that calculates the rate code r(t) from a spike train x(t).

29 If you wanted to show that the spikes encode the stimulus variations, what type of rate code would you need?

30 Exercise. You want to measure stimulus response functions of visual, auditory, taste, olfactory and touch receptors. For each type of receptor, define the axis of variation for the stimulus you would use and the response measure you would use. Draw the hypothetical stimulus-response functions. What would happen when you change the stimulus amplitude?

31 Common ways to represent neural spike trains in response to given stimuli ) Raster plots 2) Peri-stimulus histograms 3) Spike-triggered averages 4) Interspike-interval distributions Lecture 2: Can a Neural Code be Defined?

32 ) Rasterplots Lecture 2: Can a Neural Code be Defined? 2) Peristimulus histogram

33 Lecture 2: Can a Neural Code be Defined? 3) Spike triggered averages very useful for periodic signals!

34 Lecture 2: Can a Neural Code be Defined? 4) Interspike interval distributions # of occurrences Interspike interval

35 Lecture 2: Can a Neural Code be Defined? It is important: - to define your stimulus of interest - to define the time scale of interest - to define your sampling step

36 Lecture 2: Can a Neural Code be Defined? Can "neural coding" be defined at all? - Correlation between observed neural activity and some experimental manipulation of interest - Can be defined from the point of view of the observer, or from the point of view of the organism - Experimental manipulations will always change "the code" -Other?

37 Reading for Monday Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex John K. Chapin, Karen A. Moxon, Ronald S. Markowitz and Miguel A. L. Nicolelis2

38 ) Extracellular recordings in awake behaving rats

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