Neurons and conductance-based models

Transcription

1 Neurons and conductance-based models Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering, KAIST

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

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8 Prototypical Neuron This illustration represents a prototypical (i.e., idealized) neuron. Dendrites receive incoming information, nerve impulses are transmitted down the axon, and the terminal buttons release neurotransmitters which stimulate other cells. - Dendrites - Cell body (soma) - Nucleus - Axon - Myelin sheath - Nodes of Ranvier - Arborizations - Terminal buttons

9 Neurons are specialized cells

10 Neuronal structures

11 1mm 10, neurons Signal: 3 km wires action potential (spike) action potential

12 Molecular l basis -70mV Na + action potential K + Ions/proteins Ca 2+

13 Phenomenology of spike generation j i Spike reception: EPSP, summation of EPSPs u i threshold -> Spike Threshold Spike emission (Action potential) Spike reception: EPSP Elements of Neuronal Dynamics

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15 Local field potential or EEG recordings

16 Types of Chemical Synapses

17 Synaptic clefts

18 EPSP and IPSP modeling

19 Complex spatiotemporal dynamics in the Brain

20 Several sources of complexity in EEG

21 Complex rhythms and oscillations in the brain

22 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 behavior Like functional specialization, functional integration ti occurs at multiple spatial and temporal scales.

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24 Neural encoding and decoding Neural encoding Neural encoding refers to h the map from to stimulus to response. Neural decoding Neural decoding di refers to the reverse map from response to stimulus.

25 Recording neuronal responses Membrane potentials are measured by connecting a hollow glass electrode filled with a conducting electrolyte to a neuron, and compare the potential it records with that of a reference electrode placed in the extracellular medium.

26 Firing rates The spike-count rate The time-dependent d t firing i rate The average firing rate

27 Time-dependent firing rates

28 Measuring firing rates Linear filter and filter kernel Counting spikes in pre- assigned bins produces a firing-rate estimate that depends not only on the size the time bins but also on their placement.

29 Spike-triggered Average

30 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

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

32 Burst as a information carrier

33 Tonic and phasic activity A neuron is said to exhibit a tonic activity when it fires a series of single action potentials randomly.

34 Tonic and phasic activity A neuron is said to fire a burst of spikes (phasic h i activity) it ) when it fires two or more action potentials followed by a period of quiescence. A burst of two spikes is called a doublet, of three spikes is called a triplet, four - quadruplet, etc.

35 Examples 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. CH: Chattering neurons can fire highfrequency 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.

36 Examples of bursting neurons Hippocampus LTB: Low-threshold bursters fire highfrequency bursts in response to injected pulses of current. Some of these neurons burst spontaneously. These are pyramidal neurons in CA1 region. HTB: High-threshold bursting neurons fire bursts only in response to strong long pulses of current. (fyi, fpp: fast prepotentials)

37 Examples of bursting neurons Thalamus TC: Thalamocortical neurons can fire bursts if inhibited and then released from inhibition. This rebound burst is often called a low-threshold spike. Some fire bursts spontaneously in response to tonic inhibition. RTN: Reticular thalamic nucleus inhibitory neurons have bursting properties similar to those of TC cells.

38 Examples of bursting neurons 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.

39 Other structures Examples of bursting cells pre-bot: Respiratory neurons in pre-botzinger complex fire rhythmic bursts that control animal respiration cycle. MesV: Some Mesencephalic V neurons in brainstem may fire rhythmic bursts when slightly depolarized above the threshold. AB: 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.

40 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.

41 Detection of bursts It 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. 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.

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

43 Bursts s as a Unit of Neuronal Information o Bursts are more reliable than single spikes in evoking 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 spikes, i.e., a burst, synaptic release is more likely. Bursts facilitate transmitter release whereas single spikes do not. A synapse with strong short-term 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 the effect of the last few spikes may be quite strong. Bursts evoke long-term potentiation and hence affect synaptic plasticity much greater, or differently than single spikes (Lisman 1997).

44 Bursts as a Unit of Neuronal Information Bursts have higher signal-to-noise noise ratio than single spikes. Burst threshold is higher than spike threshold, i.e., generation of bursts requires stronger inputs. 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. Some bursts resonate with oscillations and elicit a response, others do not, depending on the interburst frequency. 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 resonant interspike frequency. Such a burst evokes just enough facilitation, but not too much depression, so its effect on the postsynaptic target is maximal.

45 Bursts s as a Unit of Neuronal Information o Bursts encode different features of sensory input than single spikes. For example, neurons in the electrosensory lateral-line 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 interspike intervals within a burst. Burst input is more likely to have a stronger impact on the postsynaptic cell than single spike input, so some believe that bursts are all-or-none events, whereas single spikes may be noise.

46 Bursting as an information carrier of temporal spiking patterns of nigral dopamine neurons (a) Dopamine neurons in substantia nigra Substantia nigra, a region of the basal ganglia that is rich in dopamine-containing neurons, is thought to be etiologies of Parkinson s disease, Schizophrenia, Tourette's syndrome etc.

47 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)

48 No determinism of non-bursting DA neurons surrogat counts/bin (D2) nsional complexity raw ISI data ms e c Histogram Dime Embedding dimension Embedding dim. vs. D2 dlnc (r)/dlnr d=5 d=7 d=9 d=13 d=11 d= lnr D2s of ISI data of DA neurons C(r)/dlnr dln d=5 d=7 d=9 d=11 d=13 d= lnr D2s of surrogate ISI data

49 Nonlinear determinism of bursting DA neurons counts/bin y (D2) nsional Complexity Dime surrogat raw ISI data 20 2 dlnc (r)/dlnr ms e c Histogram d=5 d=7 d=13 d=15 d=9 d= lnr D2s of ISI data of DA neurons dlnc (r)/dlnr d=5 d=7 Embedding dimension Embedding dim. vs. D2 d=9 d=11 d=13 d= lnr D2s of ISI surrogate data

50 The source of nonlinear determinism in ISI firing i patterns of DA neurons Materials 7 Male Sprague-Dawley rats anesthetized with chloral hydrate Original ISI (a) Non-bursting neurons (3/7) (b) Bursting neurons (4/7) Burst time series Methods (ISI <80ms, 160ms) Single spike time series (a) Estimation of correlation dimension (b) Surrogate data method (c) Burst separation method

51 Nonlinear determinism of burst time series (r)/dlnr d=15 d=13 d=11 4 d=9 3 d=7 2 d= lnr dlnc 7 dlnc ( r ) / d l n r d=15 d=13 d=11 d=9 d=7 d= lnr D2s of ISI burst time series D2s of its surrogate ISI time series

52 No determinism of single spike time series nc(r )/dln r d l n d=15 11 d=13 10 d=11 9 d=9 8 7 d=7 6 d= lnr nc (r)/dlnr dln d= d=13 10 d=11 9 d=9 8 7 d=7 6 d= lnr D2s of ISI single spike time series D2s of its surrogate ISI time series

53 Nonlinear determinism of inter-burst interval data nc(r )/dln r d l n d=5 d=7 d=9 d=11 d=13 d= lnr nc(r)/dlnr dln d=5 d=7 d=13 d=9 d=11 d= lnr D2s of IBI data D2s of surrogate IBI data

54 Summary 1. Bursting DA neurons had nonlinear determinism in ISI firing patterns, whereas non-bursting DA neurons did not. 2B 2. Burst ttime series extracted tdfrom 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 temporal spiking patterns of nigral ldopamine neurons. J Neurophysiology (revised)

55 Spike Train Statistics i

56 Spike-train Statistics The probability density: the probability that a spike occurs 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. Point process: A stochastic ti process that t generates a sequence of events, such as action potentials. Renewal process: A stochastic ti process that t generates a sequence of events with the intervals between successive events are independent. Poisson process: A stochastic process that generates a sequence of events with no dependence at all on preceding events, so that the events themselves are statistically independent.

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

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

59 The 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 during a short interval of duration Δt is r est (t) Δt.

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

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64 Fano factor: Variability of MT neurons in alert macaque monkeys F( T ) var[ Ni ( T )] N ( T ) i

65 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 mean. F( T ) var[ Ni ( T )] N ( T ) The FF of a fractal stochastic process takes the power-law form (0< F <1) for large counting time T, while it tends to stay in a constant value independent of T for a renewal process. The F is considered as the fractal exponent (scaling exponent) of the point process. The power-law form implies that the fluctuations in the firing rate converge relatively slowly as T is increased. i

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

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

68 Fano factor: Variability of MT neurons in alert macaque monkeys F( T ) var[ Ni ( T )] N ( T ) i

69 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 mean. F( T ) var[ Ni ( T )] N ( T ) The FF of a fractal stochastic process takes the power-law form (0< F <1) for large counting time T, while it tends to stay in a constant value independent of T for a renewal process. The F is considered as the fractal exponent (scaling exponent) of the point process. The power-law form implies that the fluctuations in the firing rate converge relatively slowly as T is increased. i

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71 Types of Chemical Synapses

72 Synaptic clefts

73 EPSP and IPSP modeling

74 Spike Response Model Spike emission j ^ i t t i Spike reception: EPSP u i f Spike reception: EPSP t t j Spike emission: AP ^ t t i t t j Last spike of i All spikes, all neurons f t t ^ u t t t w linear u i t i j f u t ^ i Firing: t w ij t t j t i threshold f j

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82 Hodgkin-Huxley Model C du C dt 100 inside mv g K 0 g Na I I Na g Na 3 m h( u E g l Na ) g K n I K 4 ( u Ion channels E K ) g l Ion pump Ileak ( u E l ) Ka Na outside stimulus I( t) dh dm dn hn m h nm 0 ( u) ( ) 0 u dt dt h(u n(u m(u) )

83 Hodgkin-Huxley Model pulse input I(t) inside Ka C du dt g Na I Na 3 m h( u dh dm dn hn m h nm 0 ( u) ( ) 0 u dt dt h(u n(u m(u) ) E Na ) g K n I K 4 ( u Ion channels E K ) g l Ion pump Ileak ( u E m 0 (u) h (u) h 0 (u) m (u) u l ) Na outside stimulus I( t) u

84 Hodgkin-Huxley Model refractoriness 100 Action potential mv 0 Strong stimulus strong stimuli 0 ms 20

85 Hodgkin-Huxley Model 100 mv Stimulation with time-dependent input current 0 I(t)

86 Hodgkin-Huxley Model mv mv 0 0 I(t) mv 5 h 0 Subthreshold response -5 Spike

87 Integrate-and-fire Model j i Spike emission I u i Spike reception: EPSP reset t t j f j d dt u i u i t u i RI(t) ) linear Fire+resetthreshold

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