(Boring) overview of phenomenological rules for synaptic plasticity

Transcription

1 (Boring) overview of phenomenological rules for synapic plasiciy Luba Benuskova Deparmen of Compuer Science Universiy of Oago, New Zealand

2 Ouline This alk will be abou he so-called phenomenological rules of synapic plasiciy (= rules of changes of synapic weighs) in biological neurons. Phenomenological rules aemp o capure he phenomenon of synapic plasiciy on a higher level wihou going ino deails abou molecular and biophysical processes ha underlie hese changes in synapses (albei rying o have hese in mind as much as possible). The relaionship beween phenomenological rules of synapic plasiciy and more deailed biophysical and biochemical models is similar o he relaionship beween hermodynamic equaions and equaions of saisical physics. 2

3 When an axon of cell A is near enough o excie a cell B and repeaedly or persisenly akes par in firing i, some growh process or meabolic change akes place in one or boh cells such ha A's efficiency, as one of he cells firing B, is increased. Hebb rule (1949) Cell A Cell C Oupu of cell B Neurons ha fire ogeher wire ogeher. Cell A Cell C Oupu of cell B Neurons ha fire ou of sync lose heir link. 3

4 Hebb rule: mahemaical formulas w j x j y y w j j x j The problem wih weighs growing o infiniy has been solved by modificaions like Adding various forms of a decay erm (e.g. Oja s rule) or Weigh re-normalizaion afer each updae or Seing up he maximal value of he weigh. However, numerous neurobiological experimens have brough resuls ha were in conradicion wih he basic Hebb posulae. Therefore a new insigh was needed. 4

5 ), ( M j j y x w 2 2 ) ( y y E M d e y ) / ( 2 0 ) ( 1 Bienensock, Cooper, Munro (BCM, 1982) j j x j y w ) ( ), ( M M y y y 5

6 Resuls for somaosensory corex of ras [Benuskova e al., PNAS 1994, 2001] Normal corex Impaired corex Normal corex Impaired corex 6

7 Experimenal evidence for sliding M METAPLASTICITY: Posiion of M depends on he neuron s pas aciviy (Term coined by Cliff Abraham and Mark Bear, TINS, 1996) 7

8 LTP/LTD = long-erm poeniaion/depression LTP/LTD are he gold sandard synapic models for mammalian memory mechanisms for 4 decades; LTP/LTD occur in hippocampus and in neocorex, which are brain regions involved in formaion of long-erm memories; LTP/LTD are long-lasing synapic changes; can las for hours, days, weeks even monhs; LTP/LTD are synapic aciviy-dependen. There is a moving LTD/LTP hreshold ha depends on he average of possynapic aciviy 8

9 Proocol for inducion of LTP Measuring elecrode Simulaing elecrode Simulaion es eanus hours EPSP before eanus afer eanus 9

10 LTP and LTD depends on frequency of eanus The same synapse can become poeniaed or depressed based on frequency of eanus: high frequencies ~ 100 Hz induce LTP and low frequencies ~ 110 Hz induce LTD 10

11 Timing (Markram e al., Science, 1997) In 1997, a new phenomenon was discovered ha he sign and magniude of synapic weigh change depend also on he relaive iming of pre- and possynapic spikes. Experimenal proocol of Spike-Timing Dependen Plasiciy. Pre and Pos-synapic neurons are forced o emi spikes wih a pre-defined ime difference, while he modificaion of he synapic srengh is moniored. 11

12 STDP: spike-iming dependen plasiciy Depending on he precise ime difference beween pre- and pos-synapic spike, he synapic weigh can be eiher depressed or poeniaed and he magniude of change depends on. w A e / w A e / = pos pre (ms)

13 Bu which spike pairings conribue? (a) Symmeric ineracion each presynapic spike is paired wih he las possynapic spike and each possynapic spike is paired wih he las presynapic spike. (b) Presynapic cenred ineracion each presynapic spike is paired wih he las possynapic spike and he nex possynapic spike. w = w + w (c) Reduced symmeric ineracion he same as in (a) bu only he closes pairings are considered. 13

14 STDP fails I has soon become apparen ha he STDP fails o accoun for a number of neurobiological experimens ha involve frequency based proocols. (Assumpion: if STDP is universal hen i underlies all forms of synapic plasiciy.) Over las 10 yrs, abou 50 modificaions of he basic rule have been proposed (for a review see Chrisian G. Mayr and Johannes Parzsch, Froniers in Synapic Plasiciy, doi: /fnsyn ). E.g., one of he recen modificaions is he suppression model of Froemke e al. (2006), which proposes ha A+ and A scale as a funcion of he complee hisory of he presynapic spike rain (wha would be he biological mechanism for his is quie quesionable). 14

15 Pfiser & Gersner s 3ple model w hidden variables ( 06) Schemes of he riple learning rules. A, Schemaic of he wo erms conribuing o LTD conrolled by A 2 and A 3 and he LTP erms conrolled by A + 2 and A + 3. A presynapic spike afer a possynapic one (pospre) induces LTD if he emporal difference is no much larger han. The presence of a previous presynapic spike gives an addiional conribuion (2-pre-1-pos riple erm, A 3) if he inerval beween he wo presynapic spikes is no much larger han x. Similarly, he riple erm for LTP depends on one presynapic spike bu wo possynapic spikes. The presynapic spike mus occur before he second possynapic one wih a emporal difference no much larger han +. B, and C, ime courses of hidden variables o and r. 15

16 Pfiser & Gersner s 3ple model w hidden variables ( 06) The weigh decreases afer presynapic spike arrival by an amoun ha is proporional o he value of he (hidden) possynapic variable o 1 bu depends also on he value of he presynapic deecor variable r 2. Hence, presynapic spike arrival a ime pre riggers a change w( ) w( ) o ( ) pre A A r ( ) if 1 A possynapic spike a ime pos riggers a change ha depends on he presynapic variable r 1 and he second possynapic variable o 2 as follows: w( ) w( ) r ( ) 2 2 pos A Ao ( ) if 1 Here all A s are consan ampliudes of change and variables o s and r s obey here own differenial equaions, and is a small posiive consan. 16

17 Criique of STDP as a unifying principle All hese modificaions of STDP explain resuls of differen experimenal proocols, differen experimenal condiions (in viro vs. in vivo, ec), and experimens in differen brain areas and sub-areas. Lisman, J., and Spruson, N. (2010). Fron. Syn. Neurosci. doi: /fnsyn , argued ha possynapic depolarizaion raher han a spike is necessary and sufficien for he explanaion of mos experimenal resuls ha have usually been inerpreed wihin he STDP framework. Direc evidence for STDP in vivo is limied. The sudies use longlasing large-ampliude possynapic poenials (PSP), and pairing usually involves muliple possynapic spikes or high repeiion frequencies. 17

18 Clopah, Büsing, Vasilaki, Gersner (Na. Neurosci. 2010) (a) The synapic weigh is decreased if a presynapic spike x (green) arrives when he low-pass-filered value ū (magena) of he membrane poenial is above θ (dashed horizonal line). (b) The synapic weigh is increased if he membrane poenial u (black) is above a hreshold θ + and he low-pass-filered value of he membrane poenial ū + (blue) is higher han a hreshold θ and he presynapic low-pass filer x (orange) is nonzero. 18

19 Volage-based STDP wih homeosasis The final weigh change formula in combinaion wih he hard bounds w min w w max is w A LTD ( u ) X ( u ) A x( u ) ( u ) LTP Where A LTP, θ and θ + are consans, A LTD is proporional o he average of a recen possynapic volage, i.e. A LTD = A 0 <u> (homeosasis), variable X is he series of presynapic spikes occurring a imes n, i.e. X ( ) ( ) n n And all oher membrane volage u variables obey exponenial differenial equaions. 19

20 Our conribuion o he chaos Us: Me, Cliff Abraham (Oago U) + Peer Jedlička (Goehe U) + our sudens (Azam Shirrafi Ardekani, Nick Hananeia) Our sraegy: Keep i simple as possible, bu no any more simple. 20

21 STDP leads o BCM frequency hreshold In 2003, Izhikevich and Desai showed he presynapically cenered (scheme b, slide 13) classical pair-wise STDP yields LTD / LTP hreshold in he frequency domain: = 0 M Ampliudes A s and decays s of poeniaion and depression windows, are consans. However, in he original BCM heory, M changes as a funcion of he average previous aciviy of a neuron. 21

22 STDP wih meaplasiciy Benuskova and Abraham (2007) inroduced changing LTD/LTP ampliudes according o average possynapic aciviy: spike ic no possynap here is if 0 ic spike here is a possynap if 1 ) ' ( where ) ( )exp ( 0 c d c c c 22 c A A c A A 0 0 / / e A w e A w * Works also when c is replaced wih PSP!

23 Experimenal daa: eanus of MPP leads o homosynapic poeniaion of MPP and heerosynapic depression of LPP Hippocampus [Abraham e al, PNAS 2001] CA3 GC CA1 To enorhinal corex (EC) To subiculum from cec Denae gyrus mpp lpp poeniaed MPP Synapic change LPP depressed hours 23

24 Izhikevich model of spiking neuron v u if v 5v 140u I a( bv u) v AP, hen u v c u d lpp mpp I = s mpp w mpp N mpp + s lpp w lpp N lpp s mpp / lpp 1 0 if here is presynapic oherwise spike 24

25 Assumpions of he model The STDP rule is allowed o dynamically change he ampliudes of LTP and LTD according o he previous mean spike coun of he possynapic neuron or he average of previous membrane volage over shor ime ~ 1min (he resuls are he same). We simulae he pre- and possynapic sponaneous spiking aciviy, which is random bu correlaed beween LPP and MPP a he hea frequency because experimens were done in vivo. We emporarily de-correlae he spiking aciviy of MPP and LPP pahways during LTP inducion (Benuskova & Abraham, J. Comp. Neurosci., 2007). 25

26 Resuls of STDP wih meaplasiciy (homeosasis) Teanus consised of 1440, 50 or 10 rains of en pulses a 400 Hz. I was delivered in burss of 5 6 rains a 1-s inervals, wih s beween burss, depending on he proocol. a b MPP MPP LPP LPP c d MPP LPP 26

27 Predicion from his model: if he sponaneous aciviy (noise) is blocked so is he heero-plasiciy A 100 Medial pah Weigh (% change) B Weigh (% change) Laeral pah HFS conrol no laeral aciviy Abraham WC, Logan B, Wolff A, Benuskova L : "Heerosynapic" LTD in he denae gyrus of anesheized ra requires homosynapic aciviy. Journal of Neurophysiology, 98: , Time (min) 27

28 Inerplay beween frequency and STDP Simulaions of in viro resuls from Lin e al., J. Eur. Neuroscience,

29 Comparmenal model of granule cell Aradi and Holmes (1999) developed a realisic comparmenal model of he granule cell and Schmid-Hieber implemened i in NEURON. In he reduced morphology model here are six regions of he DG cell having differen disribuions of volage-acivaed channels he soma, axon, granule cell layer dendries, proximal, middle, and disal dendries. Parameers l denoes he lengh in m of a segmen where channels are disribued uniformly, and n is he number of comparmens. 150 MPP synapses are creaed a he middle pars of he dendries and 150 LPP synapse are creaed a he disal pars of he dendries. 29

30 Comparmenal model of granule cell Differenial equaion for he membrane volage reads: 30

31 Comparmenal model of granule cell Equaions for he exciaory synapic curren are as follows: I X X syn( e) gsyn( e) ( Esyn( e) Vk ) g X syn X ( e) w exp exp 1, X 2, X Where X sands for MPP or LPP, E is he equilibrium poenial for exciaory synapses, V k is he membrane volage a synapse k, g is membrane conducance, which obeys he double exponenial equaion wih rise 2 and decay 1 consans. Parameer w is he synapic weigh ha is updaed according o our STDP rule wih meaplasiciy (implemened by Peer Jedlička). 31

32 STDP wih meaplasiciy Since now we have dendries wih passive membrane properies and spaio-emporal summaion of PSPs, DT is calculaed as = pos pre Where pos = ime when V k > -37 mv. This can happen eiher as a resul of backpropagaing AP and/ or spaio-emporal summaion of PSPs. w w A A e e / / A A A A 0 0 c c c c ( ) c( )exp d 0 where c( ') 1 0 if if here is a possynap ic spike here is no possynap ic spike * Noe: Works also when c is replaced wih PSP. 32

33 Resuls 33

34 Summary Hebbian rules BCM rule STDP rules Possynapic volage-based rules Wha s nex??? 34

35 Conclusion? As far as he laws of mahemaics refer o realiy, hey are no cerain, and as far as hey are cerain, hey do no refer o realiy. (Alber Einsein) 35