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Coding of Temporal Information by Activity-Dependent Synapses

Coding of Temporal Information by Activity-Dependent Synapses. A study of the biological models with an extension to an electrical engineering model Whei Hsueh, Angela Gee, and Jonah Lehrer. December 2002. Computational Neuroscience I Aurel Lazar, Rafael Yuste. 1. Project Goals.

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Coding of Temporal Information by Activity-Dependent Synapses

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  1. Coding of Temporal Information by Activity-Dependent Synapses A study of the biological models with an extension to an electrical engineering model Whei Hsueh, Angela Gee, and Jonah Lehrer December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 1

  2. Project Goals “Coding of Temporal Information by Activity-Dependent Synpases”Galit Fuhrman, Idan Segev, Henry Markram, and MishaTsodyksThe American Physiological Society, 2002 1) to find the optimal conditions in order for the postsynaptic neuron to encode the most temporal information from the presynaptic neuron for a depressing synapse 2) model an optimal depressing synapse using a low pass filter December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 2

  3. Outline for Presentation Neurobiology Background - depressing synapses - biological explanations Probabilistic Model for Depressing Synapses- theoretical and biological description- optimal parameters- MATLAB simulation results Model Depressing Synapse as a RC Low-Pass Filter- RC Low-Pass Filter design parameters - simulation results December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 3

  4. Key Biological Questions 1) What are the bio-physical parameters of the synapse? 2) How does the information encoded for by the neuron depend on the bio-physical parameters of the synapse? December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 4

  5. Communication Between Two Neurons Via the Synapse Presynaptic neuron Postsynaptic neuron Postsynaptic response (PSR) Input spike train Information component in PSR tells us about the timing of prior presynaptic spikes December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 5

  6. Information Encoded by the Neuron •Definition:The magnitude of the resulting conductance change in the post-synaptic neuron. •Release Probability:Result of transmitter release probability (itself a function of the time constant of recovery from depression) •History Dependence:Can depend on the history of activity at a synapse December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 6

  7. Depressing Synapse •In depressive short term plasticity, pulses between inter-cortical neurons dramatically decrease in amplitude upon repeated activation of the synpatic conductance. •The short term synaptic dynamics in the neo-cortex are specific to the types of neurons involved. For example, pyramidal to pyramidal connections typically consist of depressing synapses. Depression of excitatory intracortical synapse December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 7

  8. Structure of Pyramidal Neurons Can Contribute to Depression •Pyramidal NeuronsPyramidal neurons are projection neurons whose axons project to other brain regions as well as interconnecting neurons in local areas. In addition, they have interconnections among their own dendritic trees. December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 8

  9. Structure of Pyramidal Neurons Can Contribute to Depression •Pyramidal Dendritic TreeThe compartmentalization and ultra-sensitivity of the pyramidal dendritic tree (defined by the small amplitude of the signal) may be important for selectively altering the strength of synaptic connections during learning and memory. December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 9

  10. Additional Thoughts Other possible biological explanations for the low amplitude of the signal in depressing synapses: 1) reduced rate of vesicle recycling 2) reduced calcium influx due to decreased densities of calcium channels on depressing dendrites December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 10

  11. Probabilistic Model for Synapses Presynaptic neuron Postsynaptic neuron synapse Vesicles with neurotransmitters at N release sites Neurotransmitter receptors December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 11

  12. Probabilistic Model for Synapses Action Potential December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 12

  13. Probabilistic Model for Synapses USE USE : fraction of available pool utilized ~ probability of release given that the site has a vessicle December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 13

  14. Probabilistic Model for Synapses December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 14

  15. Probabilistic Model for Synapses Postsynaptic Response (PSR) December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 15

  16. Probabilistic Model for Synapses rec rec: time it takes a vesicle to recycle after synaptic depression (time recovery constant)

  17. Coding of Info. by Depressing Synapseusing the probabilistic model USE Action Potential Postsynaptic Response (PSR) rec INFO. The PSR contains temporal information about the presynaptic interspike intervals (freq. of AP train) - What are the optimal parameters for maximum information transfer across the synapse? 1. Presynaptic firing rate (AP train) 2. Fraction of available synaptic pool utilized (USE) 3. Time constant of recovery from depression(rec)

  18. Effect of presynaptic firing rate Ri = Prel*r Probability of release (Prel) * Information rate (Hz) Prel Presynaptic firing rate (r) in Hz Optimal Firing Rate:of presynaptic neuron for the most efficient transfer of information across the depressing synapse Po • Probability of release (Prel) = 1 + (1-fD) r rec • Info. Rate = Prel * r • Po = 1, fD (USE) = .6, rec = 500 msec (Dayan and Abbott, 2001) • presynaptic firing rate at which info. transfer rate starts to be independent 1/((1- fD) rec ) = 5 Hz * •fopt~ flim = 1/ USErec = 3 Hz • fopt in biological models range from 0.7-20 Hz with most below 5 Hz. (Tsodyks 2002)

  19. Probability Model:Depressed Synapses at non-optimal firing rate • Top: 0.2 hz presynpatic impulse train • Bottom:red – Pv [vesicle available for release]blue – Prel [prob of release] December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 19

  20. 1 - exp( -1 / r rec) 1 - ( 1 - USE) exp( -1 / r rec) Optimal Firing Rate Effect of presynaptic firing rate on synaptic efficacy • Fraction ofavailable synaptic efficacy (R): 1 - R USE = .59, rec= 813 msec Fraction of available synaptic efficacy (R) Fraction of utilized synaptic efficacy (1-R) • Optimal firing rate occurs at lower hz (<5) (Tsodyks 2002) R Presynaptic firing rate (r) in Hz

  21. 1 rec= USE r Po • Prel = 1 + (1-fD) r rec What is the optimal combination of synaptic parameters that maximizes info coding at a given frequency? Effect of utilized synaptic pool on information transfer rate Effect of time recovery constant on information transfer rate USE vs. rec Information rate (Hz) Information rate (Hz) rec (sec) fD = .5 r = 2 hz rec = 813 msec rec(sec) USE USE • The more you utilize the synapse, the higher the rate of info transfer. • Optimal USE = 1 • Biologically, USE is between 0.1 - 0.95 (Tsodyks 1997) • For optimal encoding, recshould be in tune with USE and r such that • The smaller the rec, the more info transfer. • Info rate = Prel * r • Biologically, recis 160 -1500 msec (Markram 1997) • Po = 1, r = 2

  22. Short Term Depression at a Cortical Synapse: Postsynaptic Responses to a Presynaptic Spike Train EPSP amplitude (mV) r = 2 hz Response number (n) EPSPn = A • Rn • USE R n+1 = Rn ( 1 – USE) exp (- t /  rec) + 1 – exp (-  t / rec)  t = .5 sec, USE = .6,  rec = 800 msec, A = 2.71 (Tsodyks 1998)

  23. MATLAB codeProbabilty of Release and Info Rate % PROBABILITY OF RELEASE AND INFORMATION RATE %(as a function of firing rate of presynaptic neuron) % Author: Angela Gee % Date: December 2002 % E4011 Final Project %variables %Prel = probability of a vessicle available for release (at average steady state, ie. at a constant firing rate of the presynaptic neuron). t = .5; %recovery time constant in sec, typical tau is 500 msec Po = 1; %initial probability of release fD = .6; %depression constant, synonymous to U (fraction of utilized available synaptic efficacy) r = 0:100; %the firing rate of presynaptic neuron (hz) %equation for Prel as a function of presynaptic firing rate (Dayan and Abbott, 2001) Prel = Po ./ (1+ (1-fD) .* r .* t); %equation for the average rate of successful transmission of information(Ri) (Dayan and Abbott, 2001) Ri = r .* Prel; %rate of info. transfer depends on probability of release %plotting presynaptic firing rate vs. probability of release (prel) and rate of successful transmission (Ri) plotyy (r, Prel, r, Ri); title ('Effect of presynaptic firing rate'); xlabel ('Presynaptic firing rate (r)'); ylabel ('Probability of Release (Prel)'); hold on December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 23

  24. MATLAB codeProbabilty of Release and Info Rate %a table of values for presynaptic neurong firing rate, release probability, rate of successful transmission of %information disp ('fire rate Prel info rate') disp ([r' Prel' Ri']) %the equation for rate (R) at which rate of transfer of information becomes independent of presynaptic firing %rate (r) Rind = 1/((1 - fD) *t ); % (Dayan and Abbott, 2001) disp (['presynaptic firing rate at which info transfer rate becomes independent: ' num2str(Rind)]) %the equation for optimal firing rate and limiting frequency (Tsodyks, 2002) Ropt = 1/(fD * t); %dependent upon synaptic parameters fD and t disp (['optimal firing rate and limiting frequency: ' num2str(Ropt)]) December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 24

  25. MATLAB code:Probability model for depressed synapses %Author: Whei Hsueh %parameters time=0:.1:30; tau_rec=.8; U=0.5; N=5; numv=0:.1:30; %variables Pv = ones(1,301); %prob. for a vesicle available for release @ any t Pr = ones(1,301); % prob. of release for every release site @ t_sp Pnves = ones(1,301); %prob for release of n vesicles C = zeros(301,1); %combo binomial coeff X = zeros(301,1); %temp variable for Cnorm input=zeros(1,301); Hx = ones(1,301); Hxy=ones(1,301); I = ones(1,301); %input impulse trainfor i = 0:4, for j = 0:49, input(26+i.*50+j) = .2 - (.2/50)*j;endend December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 25

  26. MATLAB code:Probability model for depressed synapses for i = 0:25, input(276+i) = .2 - (.2/50)*i; end for i=0:5, input(25+i.*50) = 1; end %probability for a vesicle to be available for release @ any t for i=1:300, Pv(i+1) = Pv(i) + (1-Pv(i))/tau_rec - U*Pv(i)*input(i); end %probability of release for every release site @ time of spike Pr = U.*Pv; figure, subplot 211; plot(time,input) subplot 212; plot(time, Pr, 'blue', time, Pv, 'red') xlabel('time') ylabel('probability') title('Probabilistic Model for dynamic synapses') December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 26

  27. MATLAB code:Synaptic efficiency %Effect of presynaptic firing rate on synaptic efficacy % Author: Angela Gee %variables r = [0:.5:40]; %firing rate of presynaptic neuron r = r + (r == 0) *eps; %adjust r = 0 to r = eps to avoid dividing by zero t = .800; % recovery time constant (amt. of time it takes to refill vesicles), % from biological model, estimated at 8.13 +/- 240 ms) U = .59; % utilization of available synaptic efficacy, biologically U = .59 +/- .16 %equation giving available synaptic efficacy (R) in terms of presynaptic neuron firing rate (r) (Markram et al. 1998) %this equation is telling us the fraction of available synaptic efficacy at steady state (when there is a constant given firing rate (r) frequency from the presynaptic neuron) R = ( 1 - exp( -1 ./ (r .* t))) ./ ( 1 - ( 1 - U) .* exp( -1 ./ (r .* t))); % fraction of utilized synaptic efficacy (the amount of vessicles used and no longer available to be released) UE = 1- R; %utilized efficacy = 1- R plot (r, R); %plot rate versus fraction of available synaptic efficacy title ('Effect of presynaptic firing rate on synaptic efficacy'); xlabel ('presynaptic firing rate (r)'); ylabel ('fraction of available synaptic efficacy (R)'); hold on; plot (r, UE, 'r--') % plot rate versus fraction of utilized synaptic efficacy axis ([0 40 0 1.1])

  28. MATLAB code:Postsynaptic Responses (EPSPs) %postsynaptic response generated by an AP spike train for a depressing synapse % Author: Angela Gee % Date: December 2002 % E4011 Final Project %variables U = .50; %fraction of utilized available synaptic efficacy deltat = .5; %time bewteen spikes, 2 hz = 2 spikes per sec = .5 sec between each spike t = .8; % time recovery constant A= 2.71; % absolute synaptic efficacy spikes = 0:7; % firing of 7 action potentials, 0 being the first spike fired R= zeros (1, 8); % allocating a vector for fraction of available synaptic efficacy (R) for each spike fired R(1) = 1; % initial available synaptic efficacy %firing an AP train and finding the resulting value of R for each consecutive AP (Markram et al. 1998) for n = 1:7 % firing 7 spikes R(n+1) = R(n) .* (1-U) .* exp(-deltat/t) + 1 - exp(-deltat/t); % R for each consecutive AP in the train, R decreases with each subsequent AP fired end; % postsynaptic response generated by any AP in a train (Markram et al. 1998) EPSP = A .* R .* U; %the EPSP amplitude depends on the available synaptic efficacy (R) which changes for each AP in a train December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 28

  29. Modeling as RC Low-Pass Filter • Fopt for depressing pyramidal-pyramidal synapses ranges between 0.7 and 20 Hz, with most at or below 5 Hz (Tsodyks 2002) • Limiting frequency typically in the range of 10-25 Hz (Tsodyks 1997) • May be related to the fact that most of the time neocortical neurons are active at low, spontaneous, firing rates of a few spikes per second (Tsodyks 2002) • Can be modeled as a low-pass filter (LPF), specifically a resistor-capacitor filter b/c cutoff is not as sharp (Butterworth provide more accurate and sharp cutoffs that are not necessary for these applications at this frequency)

  30. R + + in(t) C out(t) - - RC Low-Pass Filter (LPF) • Transfer function:H() = out()/in() where  = freq in rad/s • Voltage divider:H() = (1/jC) = 1 = a . R + (1/jC) 1 + jRC a + j  where a = 1/RC • Amplitude Response:|H()| = a  1  << a (a2 + 2) • Time Delaytd() = - dh = a  1  << a d a2 + 2 a December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 30

  31. Design of LPF #1 • Amplitude response variation = 2% tolerance • Time delay variation = 5% tolerance • Input impulse spike train = 20 Hz ( 23 Hz from Tsodyks 1997 paper) • fopt  5 Hz (from Tsodyks 2002 paper) • Actual cutoff frequency for our LPF f = 5.094 Hz R = 625 k + + in(t) out(t) C = 1 nF - - December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 31

  32. Results for LPF #1 December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 32

  33. Design of LPF #2 • Amplitude response variation = 2% tolerance, |H(0)|  0.98 • Time delay variation = 5% tolerance, td(0) 0.95/a • Input impulse spike train = 20 Hz ( 23 Hz from Tsodyks 1997 paper) • flimiting  25 Hz (from Tsodyks 1997 paper) • Actual cutoff frequency for our LPF f = 25.479 Hz R = 125 k + + in(t) out(t) C = 1 nF - - December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 33

  34. Results of LPF #2 December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 34

  35. MATLAB code:RC Low-Pass Filter %Demo of simple RC low pass filter%Author: Whei Hsueh%Date: December 2002%E4011 Final Project :: Fuhrmann, Segev, Markram, and Tsodyks 2002 Paper%Coding of Temporal Information by Activity-Dependent Synapses %parametersfs=20; %frequency of input impulse train signal (in Hz)R=125e3; %resistance = 625 kOhms (cutoff = 5Hz), 125 kOhms (cutoff = 25Hz)C=1e-9; %cap = 1 nFamp_tol=.02; %amplitude tolerance = 2%td_tol = .05; %time delay tolerance = 5% %variablest = 0:.001:1; %vector for time variablef = 0:1000; %vector for freq (Hz)w = 0:3000:3e6; %vector for freq (rad)H = ones(1,1001); %vector for transfer function of filtertheta = zeros(1,1001); %phase shift of filtertd = ones(1,1001); %time delay input = zeros(1,1001); %input spike trainoutput = zeros(1,1001); %outputA = ones(1,1001); %amplitude resp of filter f = w/(2*pi); December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 35

  36. MATLAB code:RC Low-Pass Filter (cont’d) %input impulse trainfor i = 0:18, for j = 0:49, input(26+i*50+j) = .2 - (.2/50)*j;endend for i = 0:25, input(976+i) = .2 - (.2/50)*i;end for i=0:19, input(25+i*50) = 1;end %transfer function & outputa = 1/(R*C); for i=1:1001, %calculating transfer function of filter %H(w) = 1/(1+jwRC) = a/(a+jw) where a=1/RC H(i) = a/(a+j.*i); %filtering the input output(i) = H(i)*input(i); %calculate amplitude response of filter A(i) = a/sqrt(a^2 + i^2); %calculate phase shift theta(i) = -atan(i/a); %calculate time delay %td(w) = -dtheta/dw = a/(w^2 + a^2) td(i) = a/(i^2 + a^2); end %plot input impulse spike trainfigure,subplot 211;plot(t,input)xlabel('time (s)')ylabel('Filter input') %plot filtered outputsubplot 212;plot(t,output,'red')xlabel('time (s)')ylabel('Filtered output') December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 36

  37. MATLAB code:RC Low-Pass Filter (cont’d) %calculate cutoff frequency%assume when w=0:% A(0) = 1, td(0)=1/a% A must be greaten than or equal to 1 - [amplitude tol]% td must be greater than or equal to (1 - [delay tol])/a %cutoff freq calculated from amp constraint (in rad/s)wc1 = a*sqrt((1/(1-(amp_tol^2)))-1); %cutoff freq calculated from td constraint (in rad/s)wc2 = a*sqrt((1/(1-td_tol))-1); %cutoff frequencies in Hzwc1f = wc1/(2*pi);wc2f = wc2/(2*pi); December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 37

  38. Significance and Conclusions Dynamic synapses can encode information about timing of preceding spikes Temporal code is used for information processing in neocortex Depressing synapses can serve as a powerful mechanism of plasticity by altering the parameters Future: look at ability of dynamic synapse to encode temporal information from many different presynaptic spike trains December 2002 Computational Neuroscience IAurel Lazar, Rafael Yuste 38

  39. References (selected) • Dayan, P. and Abbott, L. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press, Cambridge, MA. • Fuhrman, G., Segev, I., Markram, H., and Tsodyks, M. “Coding of Temporal Information by Activity-Dependent Synpases.” The American Physiological Society, 87:140-148, 2002. • Kendal, Schwartz and Jessel (2000). Principles of Neuroscience. McGraw-Hill Companies, Inc., USA • Markram, H. and Tsodyks, M. “Differential signaling via the same axon of neocortical pyramidal neurons.” Proc. Natl. Acad. Sci. USA, 95:5323-5328, 1998. • Tsodyks, M. and Markram, H.“The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability.” Proc. Natl. Acad. Sci. USA, 94:719-723, 1997

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