neuronsand conductance-based models -...

Neurons and conductance-based models

Jaeseung Jeong, Ph.DDepartment of Bio and Brain EngineeringDepartment of Bio and Brain Engineering,

KAIST

Bilateralization (양측편재화): HAROLD:Hemispheric Asymmetry Reduction in Older Adults

Prototypical Neuron

This illustration represents a prototypicalThis illustration represents a prototypical(i.e., idealized) neuron. Dendrites receive incoming information, nerve impulses are t itt d d th d thtransmitted down the axon, and the terminal buttons release neurotransmitters which stimulate other cells.

- Dendrites- Cell body (soma)- Nucleus- Axon- Myelin sheathMyelin sheath- Nodes of Ranvier- Arborizations- Terminal buttons- Terminal buttons

Neurons are specialized cellsNeurons are specialized cells

Neuronal structuresNeuronal structures

10 000 neurons Si l10,000 neurons3 km wires

1mm

Signal:action potential (spike)

actionpotential

M l l b iMolecular basis

actionpotential

N +

-70mV

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Phenomenology of spike generation

ij

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Spike reception: EPSP,summation of EPSPs

Threshold Spike emissionThreshold Spike emission(Action potential)

Spike reception: EPSP

Elements of Neuronal Dynamics

Local field potential or EEG recordingsp g

T f Ch i l STypes of Chemical Synapses

Synaptic cleftsSynaptic clefts

EPSP and IPSP modelingEPSP and IPSP modeling

Complex spatiotemporal dynamics in the BrainComplex spatiotemporal dynamics in the Brain

Several sources of complexity in EEGp y

Complex rhythms and oscillations i th b iin the brain

The origin of brain complex dynamics: Functional segregation and integration

• While the evidence for regional specialization in the brain is overwhelming, it is clear that the information conveyed by the activity of specialized groups of neurons must be functionally integrated in order to guide adaptive behaviorLik f ti l i li ti f ti l i t ti t• Like functional specialization, functional integration occurs at multiple spatial and temporal scales.

Neural encoding and decodingNeural encoding and decoding

• Neural encodingN l di f ‘ h f i lNeural encoding refers to ‘the map from to stimulus to response.’

• Neural decodingN l d di f t ‘th fNeural decoding refers to ‘the reverse map from response to stimulus.’

Recording neuronal responsesRecording neuronal responses

Membrane potentials are measured by connecting ‘a hollow glass electrode’ filled with a conducting electrolyte to a neuron, and g y ,compare the potential it records with that of a reference electrode placed in the extracellular medium.

Firing ratesg

• The spike-count rate

h ti d d t fi i t• The time-dependent firing rate

• The average firing rate

Time dependent firing ratesTime-dependent firing rates

Measuring firing ratesMeasuring firing rates

Linear filter and filter kernel

Counting spikes in pre-assigned bins produces a assigned bins produces a firing-rate estimate that depends not only on ‘the size th ti bi ’ b t l ‘th i the time bins’ but also on ‘their placement.’

Spike triggered AverageSpike-triggered Average

Th ik t i d ti l f f th The spike-triggered average stimulus for a neuron of the electrosensory lateral-line lobe of the weakly electric fish

Single- and multiple-spike-triggered average stimuli for a blowfly H1 neuron

Burst as a information carrier

Tonic and phasic activityTonic and phasic activity

• A neuron is said to exhibit a tonic activity when it fires a series of single action potentials randomly. g y

Tonic and phasic activityTonic and phasic activity

A i id fi b t f ik ( h i ti it )• A neuron is said to fire a burst of spikes (phasic activity) when it fires two or more action potentials followed by a period of quiescence A burst of two spikes is called a doubletperiod of quiescence. A burst of two spikes is called a doublet, of three spikes is called a triplet, four - quadruplet, etc.

Examples of bursting neuronsExamples of bursting neurons

• Neocortex

IB: Intrinsically bursting neurons, if stimulated with a long pulse of dc current, fire an initial burst of spikes followed by shorter bursts, and then tonic spikes. These are predominantly pyramidal neurons in layer 5. py y

CH: Chattering neurons can fire high-f b f ik i hfrequency bursts of 3-5 spikes with a relatively short interburst period. Some call them fast rhythmic bursting (FRB) cells. These are pyramidal neurons in layer 2-4, mainly layer 3.


• Hippocampus

LTB: Low-threshold bursters fire high-frequency bursts in response to injected pulses of current. Some of these neurons burst spontaneously. These are pyramidal neurons in CA1

iregion.

HTB: High-threshold bursting neurons g gfire bursts only in response to strong long pulses of current. (fyi, fpp: fast prepotentials)p p )


• Thalamus

TC: Thalamocortical neurons can fire bursts if inhibited and then released from inhibition. This rebound burst is often called a low-threshold spike. pSome fire bursts spontaneously in response to tonic inhibition.

RTN: Reticular thalamic nucleusRTN: Reticular thalamic nucleus inhibitory neurons have bursting properties similar to those of TC cells.


• Cerebellum

PC: Purkinje cells in cerebellar slices usually fire tonically but when synaptic input is blocked they can switch to a trimodal pattern which includes a bursting phase.

Examples of bursting cellsExamples of bursting cells • Other structures

pre-Bot: Respiratory neurons in pre-Botzinger complex fire rhythmic bursts that control animal respiration cycleanimal respiration cycle.

MesV: Some Mesencephalic V neurons in brainstem may fire rhythmic bursts whenbrainstem may fire rhythmic bursts when slightly depolarized above the threshold.

AB: Anterior bursting neuron in lobsterAB: Anterior bursting neuron in lobster stomatogastric ganglion fires rhythmic bursts autonomously.

R15: Aplysia abdominal ganglion neuron R15 fires autonomous rhythmic bursts.

β-cell: Pancreatic β-cells fire rhythmic bursts that control the secretion of insulin.

• Almost every neuron can burst if stimulated or manipulated pharmacologically.

• Many neurons burst autonomously due to the interplay of fast ionic currents responsible for spiking activity and slower currents that modulate the activity.

Detection of burstsDetection of bursts

• It is relatively easy to identify bursts in response to simple stimuli such as dc stepsIt is relatively easy to identify bursts in response to simple stimuli, such as dc steps or sine waves, especially if recording intracellularly from a quiet in vitro slice. The bursts fully evolve and the hallmarks of burst responses are clear.

i li f i d f d bl i l• However, responses to sensory stimuli are often comprised of doublets or triplets embedded in spike trains. Furthermore, these responses are usually recorded extracellularly so the experimenter does not have access to the membrane potential fluctuations that are indicative of bursting. Thus, it is difficult to distinguish burst responses from random multispike events.

The statistical analysis of bursting activity

• Bimodal inter-spike interval (ISI) histograms can be indicative of burst responses. The rationale is that short ISIs occur more frequently when induced by burst d namics than o ld occ r if predicted b Poisson firing B rst spikes ith shortdynamics than would occur if predicted by Poisson firing. Burst spikes with short ISIs form the first mode while quiescent periods correspond to the longer ISIs of the second mode.

• This is true for intrinsic or forced (stimulus driven and network-induced) bursting. Furthermore, the trough between the two modes may correspond to the refractory period of an intrinsic burst or the timescale of the network-induced bursting. p g

• This method defines a criterion for burst identification so that further analysis and experimentation can determine the mechanism and function of the bursts.

Bursts as a Unit of Neuronal Informationu s s s U o Neu o o o• Bursts are more reliable than single spikes in

evoking responses in postsynaptic cells Indeedevoking responses in postsynaptic cells. Indeed, excitatory post-synaptic potentials (EPSP) from each spike in a burst add up and may result in a superthreshold EPSP.

• Bursts overcome synaptic transmission failure.Indeed, postsynaptic responses to a single presynaptic spike may fail (release does not occur), however in response to a bombardment of spikeshowever in response to a bombardment of spikes, i.e., a burst, synaptic release is more likely.

• Bursts facilitate transmitter release whereas single spikes do not. A synapse with strong short-termspikes do not. A synapse with strong short term facilitation would be insensitive to single spikes or even short bursts, but not to longer bursts. Each spike in the longer burst facilitates the synapse so th ff t f th l t f ik b itthe effect of the last few spikes may be quite strong.

• Bursts evoke long-term potentiation and hence affect synaptic plasticity much greater oraffect synaptic plasticity much greater, or differently than single spikes (Lisman 1997).

Bursts as a Unit of Neuronal InformationBursts as a Unit of Neuronal Information• Bursts have higher signal-to-noise ratio than single spikes. BurstBursts have higher signal to noise ratio than single spikes. Burst

threshold is higher than spike threshold, i.e., generation of bursts requires stronger inputs.

b d f l i i i if h i• Bursts can be used for selective communication if the postsynaptic cells have subthreshold oscillations of membrane potential. Such cells are sensitive to the frequency content of the input. Somecells are sensitive to the frequency content of the input. Some bursts resonate with oscillations and elicit a response, others do not, depending on the interburst frequency.

i h h i l i i ki• Bursts can resonate with short-term synaptic plasticity making a synapse a band-pass filter. A synapse having short-term facilitation and depression is most sensitive to a burst having certain resonantand depression is most sensitive to a burst having certain resonant interspike frequency. Such a burst evokes just enough facilitation, but not too much depression, so its effect on the postsynaptic target i i lis maximal.

Bursts as a Unit of Neuronal Informationu s s s U o Neu o o o

• Bursts encode different features of sensory input than single spikes.For example neurons in the electrosensory lateral line lobe (ELL)For example, neurons in the electrosensory lateral-line lobe (ELL) of weakly electric fish fire network induced-bursts in response to communication signals and single spikes in response to prey signals.

• Bursts have more informational content than single spikes when analyzed as unitary events. This information may be encoded into the burst duration or in the fine temporal structure of interspikethe burst duration or in the fine temporal structure of interspike intervals within a burst.

• Burst input is more likely to have a stronger impact on the p y g ppostsynaptic cell than single spike input, so some believe that bursts are all-or-none events, whereas single spikes may be noise.

Bursting as an information carrier of temporal iki tt f i l d ispiking patterns of nigral dopamine neurons

(a) Dopamine neurons in substantia nigra

Substantia nigra, a region of the basal ganglia that is rich indopamine-containing neurons, is thought to be etiologies ofParkinson’s disease, Schizophrenia, Tourette's syndrome etc.

Electrophysiology of DA neurons in substantia nigra

• Irregular and complex single spiking and bursting states in vivo

• The presence of nonlinear deterministic structure in ISI firing patterns (Hoffman et al. Biophysical J, 1995)

• Deterministic structure of ISI data produced by nigral DA neurons reflects• Deterministic structure of ISI data produced by nigral DA neurons reflects interactions with forebrain structures (Hoffman et al. Synapse 2000)

No determinism of non-bursting DA neurons

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Nonlinear determinism of bursting DA neurons

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The source of nonlinear determinism i S fi i f Ain ISI firing patterns of DA neurons

Materials7 Male Sprague-Dawley rats

(a) Non-bursting neurons (3/7)

anesthetized with chloral hydrate Original ISI

(b) Bursting neurons (4/7)

(ISI

Nonlinear determinism of burst time seriesNonlinear determinism of burst time series

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No determinism of single spike time seriesNo determinism of single spike time series

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Nonlinear determinism of interNonlinear determinism of inter--burst interval databurst interval data

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SummarySummary

1 Bursting DA neurons had nonlinear determinism in ISI firing1. Bursting DA neurons had nonlinear determinism in ISI firing patterns, whereas non-bursting DA neurons did not.

2 B t ti i t t d f b ti DA h d2. Burst time series extracted from bursting DA neurons showed nonlinear determinism, whereas single spike time series did not.

3. Inter-burst interval data of bursting neurons demonstrated nonlinear deterministic structure.

These findings suggest that bursts are likely source of nonlinear determinism in the ISI data of DA neurons.

Jeong et al. Bursting as a source of nonlinear determinism in t l iki tt f i l d i Jtemporal spiking patterns of nigral dopamine neurons. J Neurophysiology (revised)

S ik T i S i iSpike Train Statistics

Spike-train Statistics• The probability density: the probability that a spike occurs

within a specific value (cf histogram)within a specific value. (cf. histogram)• The firing rate r(t) determines the probability of firing a single

spike in a small interval around the time, but r(t) is not in general sufficient information to predict the probabilities of spike sequences.

P i t A t h ti th t t • Point process: A stochastic process that generates a sequence of events, such as action potentials.

R l A t h ti th t t • Renewal process: A stochastic process that generates a sequence of events with the intervals between successive events are independent.p

•Poisson process: A stochastic process that generates a sequence of events with no dependence at all on preceding q p p gevents, so that the events themselves are statistically independent.

The probability that a homogeneous Poisson process

: Poisson distribution

The probability that a homogeneous Poisson process generates n spikes in a time period of duration T

Autocorrelation and cross correlation histograms for Autocorrelation and cross-correlation histograms for neurons in the primary visual cortex of a cat

The Poisson Spike GeneratorThe Poisson Spike Generator

A simple procedure for generating spikes in a computer program is based on the fact that the estimated probability of firing a spike based on the fact that the estimated probability of firing a spike during a short interval of duration Δt is rest(t) Δt.

I t ik i t l di t ib ti f MT Interspike interval distribution from an MT neuron

Fano factor: Variability of MT neurons in alert macaque monkeys

)()](var[)(

TNTNTF

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Fano factor (Allan Factor)

The Fano factor (FF) is the ratio of the variance of the number of spiking events in a counting number to the meannumber to the mean.

)()](var[)(

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The FF of a fractal stochastic process takes the power-law form (0< F

I t ik i t l di t ib ti f MT Interspike interval distribution from an MT neuron

Coefficients of variation for a large number of V1 and MT neurons

Fano factor: Variability of MT neurons in alert macaque monkeys

)()](var[)(

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The Fano factor (FF) is the ratio of the variance of the number of spiking events in a counting number to the meannumber to the mean.

)()](var[)(

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The FF of a fractal stochastic process takes the power-law form (0< F

T f Ch i l STypes of Chemical Synapses

Synaptic cleftsSynaptic clefts

EPSP and IPSP modelingEPSP and IPSP modeling

Spike Response Model

ij ^itt Spike emission

iui

fttSpike reception: EPSP


itt

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Spike emission: AP j ^itt

Spike emission AP

ftt ^tt tu w linearLast spike of i All spikes, all neurons

jtt itt tui j f

ijw

t tt ^linear

threshold tui Firing: tti threshold

Hodgkin-Huxley Model

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Hodgkin-Huxley ModelHodgkin-Huxley ModelHodgkin-Huxley Model

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neuronsand conductance-based models -...

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