Neural Networks with Short-Term Synaptic Dynamics (Leiden, May 23 2008) Misha Tsodyks, Weizmann Institute Mathematical Models of Short-Term Synaptic plasticity Computations in Neural Networks with Short-Term Synaptic Plasticity Experiments: Henry Markram, Eli Nelken Theory: Klaus Pawelzik, Alex Loebel

Multineuron Recording

Principles of Time-Dependency of Release Synaptic Facilitation Synaptic Depression Three Laws of Release Limited Synaptic Resources Release Dependent Depression Release Independent Facilitation AP onset Facilitation Four Parameters of Release Absolute strength Probability of release Depression time constant Facilitation time constant Depression

A Phenomenological Approach to Dynamic Synaptic Transmission 4 Key Synaptic Parameters Absolute strength Probability of release Depression time constant Facilitation time constant

Phenomenological model of synaptic depression (deterministic)

Stochastic transmission .

Binomial model of synaptic release Loebel et al, submitted

The fitting process (deterministic model)

Testing the Model experiment experiment model model

Frequency-dependence of post-synaptic response

Frequency-dependence of post-synaptic response

Frequency-dependence of post-synaptic response

Frequency-dependence of post-synaptic response Tsodyks et al, PNAS 1997

The 1/f Law of Release

Redistribution of Synaptic Efficacy

Frequency Dependence of Synaptic Modification

RSE

Shifting the Distribution of Release Probabilities

Population signal Tsodyks et al, Neural Computation 1998

Population signal

Population signal ‘High-pass filtering’ of the input rate

Steady-state signal

Tsodyks et al PNAS 1997

Synchronous change in pre-synaptic rates

Synchronous change in pre-synaptic rates

Synchronous change in pre-synaptic rates Abbott et al Science 1997

Modeling synaptic facilitation (deterministic) Markram, Wang & Tsodyks PNAS 1998

Facilitation

Frequency-dependence of post-synaptic response

Frequency-dependence of post-synaptic response

Frequency-dependence of post-synaptic response

Population signal Tsodyks et al 1998

Steady-state signal

Signaling with Facilitating Synapses SYNAPSES AS CONTEXTUAL FILTERS

A Small Circuit

Recurrent networks with synaptic depression Tsodyks et al, J. Neurosci. 2000 Loebel & Tsodyks JCNS 2002 Loebel, Nelken & Tsodyks, Frontiers in Neurosci. 2007

Simulation of Network Activity

Simulation of Network Activity

Origin of Population Spikes

Network response to stimulation

Experimental evidence for population spikes DeWeese & Zador 2006

(no inhibition, uniform connections, rate equations) Simplified model (no inhibition, uniform connections, rate equations) i J J

The rate model equations There are two sets of equations representing the excitatory units firing rate, E , and their depression factor, R :

Tone The tonic stimuli is represented by a constant shift of the {e}’s, that, when large enough, causes the network to spike and reach a new steady state

DeWeese, …, Zador 2003

Noise amplitude (Nelken et al, Nature 1999)

Extended model Loebel, Nelken & Tsodyks, 2007

Forward suppression Rotman et al, 2001

Network response to complex stimuli

Network response to complex stimuli

Neural Network Models of Working Memory Misha Tsodyks Weizmann Institute of Science Barak Blumenfeld, Son Preminger & Dov Sagi Gianluigi Mongillo & Omri Barak

Delayed memory experiments – sample to match Miyashita et al, Nature 1988

Persistent activity (Fuster ’73) Miyashita et al, Nature 1988

Neural network models of associative memory (Hopfield ’82) Memories are represented as attractors (stable states) of network dynamics. Attractor = internal representation (memory) of a stimulus in the form of stable network activity pattern Synaptic modifications => Changes in attractor landscape = long-term changes in memory Convergence to an attractor = recall of item from long-term memory into a working form

Associative memory model Hopfield Model (1982): Neurons: Memory patterns: Synaptic connections: Network dynamics:

Associative memory model Hopfield Model (1982): Neurons: Memory patterns: Synaptic modifications:

Associative memory model Hopfield Model (1982): Neurons: Memory patterns: Synaptic modifications:

Associative memory model Hopfield Model (1982): Neurons: Memory patterns: Synaptic modifications: (for each ) if Amit, Guetfriend and Sompolinsky et al 1985

Network dynamics: Convergence to an attractor Overlap Memory #

Network dynamics: Convergence to an attractor Overlap Memory #

Context-dependent representations: gradual change in the pattern Intro – morph sequence memory is a dynamics system that is constantly updated based on experience to capture changes in the environment--- morph example. the representation depends not only on the context in which things are acquired but also on the internal context – what other objects or stimuli are represented in the same system together. Visual stimuli that we are exposed to can change the representation of objects that are already stored in the system. Also suggested by associative memory models

Long-term memory for faces Friends Non Friends … … Preminger, Sagi & Tsodyks, Vision Research 2007

Experiment – Terminology Basic Friend or Non-Friend task (FNF task) Face images of faces are flashed for 200 ms for each image the subject is asked whether the image is a friend image (learned in advance) or not. 50% of images are friends, 50% non-friends, in random order; each friend is shown the same number of times. No feedback is given ? ? ? F/NF F/NF F/NF 200ms 200ms 200ms 200ms 200ms 200ms 200ms 200ms 200ms

Morph sequence Source (friend) Target (unfamiliar) 1 … 20 … 40 … 60 … 80 … 100 Source (friend) Target (unfamiliar)

Morph effect Subject HL -------- (blue-green spectrum) days 1-18 Number of ‘Friend’ responses Bin number Preminger, Sagi & Tsodyks, Vision Research 2007

Morphed patterns – Hopfield model Continuous set of patterns

Morphed patterns – Hopfield model Continuous set of patterns Blumenfeld et al, Neuron 2006

Network dynamics: Convergence to the common attractor Overlap

Network dynamics: Convergence to the common attractor Overlap

Working memory in biologically-realistic networks (D. Amit ‘90)

Working memory in biologically-realistic networks (D. Amit ‘90)

Working memory in biologically-realistic networks (D. Amit ‘90) Brunel & Wang, J. Comp. Neurosci 2001

Working memory in biologically-realistic networks Brunel & Wang, J. Comp. Neurosci 2001

Multi-stability in recurrent networks

Multi-stability in recurrent networks Firing rate (HZ) Synaptic strength (J)

Persistent activity is time-dependent. Rainer & Miller EJN 2002

A Phenomenological Approach to Dynamic Synaptic Transmission 4 Key Synaptic Parameters Absolute strength Probability of release Depression time constant Facilitation time constant 2 Synaptic Variables Resources available (x) Release probability (u) Markram, Wang & Tsodyks PNAS 1998

Synaptic diversity in the pre-frontal cortex Wang, Markram et al, Nature Neuroscience 2006

New idea To hold short-term memories in synapses too, with pre-synaptic calcium level. Use spiking activity only when the memory is needed for processing, and/or to refresh the synapses (smth like ‘rehearsal’). Mongillo, Barak & Tsodyks 2008

Single homogeneous excitatory population – rate model

Gain function

Bifurcation diagram

Bi-stability in networks with synaptic facilitation

Attractors in networks with synaptic facilitation

Integrate and fire network simulations

Integrate and fire network simulations

Integrate and fire network simulations

Robustness and multi-item memory

Robustness and multi-item memory

Random overlapping populations

Predictions Increased pre-synaptic calcium concentration during the delay period, disassociated from increased firing rate Resistance to temporal cessation of spiking Synchronous spiking activity during the delay period Slow oscillations during the delay period (theta rhythm?).

Correlated spiking activity during delay period Constantinidis et al, J. Neurosci. 2001

Theta oscillations and working memory Lee et al, Neuron 2005

Son Preminger (WIS, Rehovot) Dov Sagi (WIS, Rehovot) Barak Blumenfeld (WIS, Rehovot) Omri Barak (WIS, Rehovot) Gianluigi Mongillo (ENS, Paris)