Final: neural circuits computation and emergence + Neurons do math

What’s an emergent property?

it occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole.

Rubins Vase

a famous set of ambiguous or bistable two-dimensional forms. it is a demonstration of the figure-ground distinction the brain makes during visual perception.

churchland/sejnowski definition of computation

the functional mapping between one state and another.

“integrate and fire” neurons

They have a resting potential in the absence of any external stimulation. They sum all the excitatory and inhibitory inputs will produce depolarization/hyperpolarization of the membrane at the spike-generating zone, which is in the axon initial segment (AIS).

Excitatory postsynaptic potentials (EPSPs)

they drive membrane potential toward spike threshold

glutamate

the primary excitatory neurotransmitter in the mamalian central nervous system

What does the opening of glutamate receptors do?

it induces depolarization of the membrane resulting in EPSPs.

Inhibitory postsynaptic potentials (IPSPs)

they are mediated by GABA

Spatial summation

the interaction of two or more synaptic inputs at a given point in time.

temporal summation

The interaction of one or more synapses across time. The closer together in time the responses are, the greater they will add to each other.

What does spike threshold determine?

Whether or not incoming stimuli are sufficient to generate an action potential. it is determined by the relative contribution of voltage-gated inward current (Na+) and outward currents (K+)

How can threshold be modulated?

enhancing the inward current decreases threshold and vice versa.

inclusive OR

input a or input b are “true” then the output will be true.

NOT function

when we have an inhibitory synapse and threshold zero . when the synapse is not active, the cell fires.

NOR function

if we have two inhibitory inputs, and only when both are active is it prevented.

How is it that the perceptron model can be “trained”?

Weights can be systematically altered to maximize the linear boundary. This is analogous to use-dependent forms of synaptic plasticity, such as long-term potentiation and depression.

passive dendrites

they are bad conductors of electrical signals - voltage attenuates and signals are low-pass filtered with distance in passive cables.

What happens when the synapse is far from the soma?

the amplitude of the response is smaller and the rise time to the peak is slower (low-pass filtered)

What happens when two synaptic inputs are located close together?

they will sum in a non-linear fashion because of a loss of driving force.

How can linear summation be achieved?

if the inputs are far apart enough from each other on passive dendrites because there is voltage attenuation with distance, there will be little interaction.

supralinear response

inward current flowing through these channels will either amplify the EPSP or possibly trigger a local spike.

sublinear response

Voltage-gated K+ conducts in the dentrites which is activated by depolarization. These channels put the “brakes” on the amplitude of the EPSP, limiting its amplitude, resulting in the prevention of firing of the cell.

What was found in the Wilfred Rall gedanken experiment?

The input that is furthest from the recording site will have the smallest amplitude and the time to peak will be delayed. the input that is closest will have the largest amplitude and will peak sooner.

What significantly influences whether or not the membrane potenital reaches spike threshold?

relative timing and relative spatial location of synaptic inputs across the dendritic tree.

What are the ways are dendritic action potentials mediated?

voltage-gated Na+ or Ca2+ channels and NMDA receptors. All of them conduct voltage-dependent inward current capable of mediating a regenerative response (action potential).

the stronger the depolarization,

the smaller the action potential

low-pass filtering

allows a response to low-frequency signals and prevents the passage of high-frequency signals.

high-pass filtering

allows a response to high-frequency signals and prevents the passage of low-frequency signals.

band pass filter

a combination of low-pass and high-pass. In the case, a response is achieved for frequencies limited to within a defined range.

Impedance

a measure of the neuron’s input/output properties and is related to the resistance of a neuron.

impedance increases as,

a function of decreasing frequency, which is low-pass filtering.

What can band pass filtering arise from?

a combination of the natural low pass filtering of the plasma membrane and the presence of a voltage gated K+ current.

fourier transform

It decomposes a function of a time-dependent signal into its composite frequencies, in a way similar to how a musical tone can be expressed as the frequencies of its constituent notes.

theta oscillations

fluctuations in the hippocamal EEG. they are believed to be important for encoding the location of the animal in both space and time

How is theta generated

one hypothesis is that cortical neurons preferentially fire at 5 Hz due to their resonance

How does the auditory system perform fourier transform?

The hair cells of the cochlea have different resonant properties along the length of the basilar membrane. Then it breaks up sound into its component frequencies.

Class I firing

it begins firing at a very low rate for a threshold level and increases asympototically to a maxiumum

Class II firing

Neurons have discontinuity at a threshold level of input; they fire at a relatively high level of output