33rd Annual International Conference of the IEEE EMBS Boston, Massachusetts USA, August 30 - September 3, 2011 Iono-Neuromorphic Implementation of Spike-Timing-Dependent Synaptic Plasticity Yicong Meng, Kuan Zhou, Joshua J. C. Monzon, and Chi-Sang Poon, Fellow, IEEE Abstract— Spike-timing-dependent plasticity (STDP) is the temporal coincidence detectors that relate the temporal ability of a synapse to increase or decrease its efficacy in pairing of glutamate release from presynaptic terminals and response to specific temporal pairing of pre- and post-synaptic the back-propagation of postsynaptic action potentials up the activities. It is widely believed that such activity-dependent dendritic tree for STDP induction. However, current long-term changes in synaptic connection strength underlie the mechanistic models of BCM synaptic plasticity cannot brain’s capacity of learning and memory. However, current phenomenological models of STDP fail to reproduce classical explain certain STDP responses, and vice versa. forms of synaptic plasticity that are based on stimulus Recently, a unified model of synaptic plasticity [8] has frequency (BCM rule) instead of timing (STDP rule). In this been proposed that captures the general biophysical paper, we implemented a novel biophysical synaptic plasticity processes governing synaptic plasticity. This model model by using analog VLSI (aVLSI) circuits biased in the considers different types of STDP characteristics reported in subthreshold regime. We show that the aVLSI synapse model the literature and relates them to the BCM rule. It provides a successfully emulates both the STDP and BCM forms of synaptic plasticity as predicted by the biophysical model. novel modeling approach that overcomes many challenges faced by previous models. Here, we propose a novel iono- I. INTRODUCTION neuromorphic (i.e., ion channels-based) analog very-large- scale-integration (aVLSI) circuit that emulates synaptic NFORMATION storage in the brain depends upon plasticity based on this unified model. I stimulus-induced synaptic modifications in neuronal networks. This phenomenon is called synaptic plasticity. It II. SYNAPTIC SYSTEM ARCHITECTURE is now well-established that synaptic connections could be strengthened or weakened depending on the relative timing The synapse based on the unified STDP model mainly between presynaptic and postsynaptic activities [1]. This produces two outputs: total calcium level and excitatory post remarkable phenomenon, generally known as spike-timing- synaptic current (EPSC) representing synaptic weight dependent plasticity (STDP), provides strong evidence for changes, where EPSC is measured in biological experiment Hebbian theory of associate learning and memory. to determine whether STDP occurs in a synapse. However, Synaptic plasticity has been extensively studied under the calcium level is difficult to measure due to limited STDP framework. Several models (e.g., [2][3]) have been experiment techniques. Our circuit provides insight about proposed aiming at reproducing the experimental data with a how the calcium level changes in the synapse. mathematical expression to reproduce the STDP Figure 1 depicts the architecture of the synapse model and characteristic phenomenologically. The limitation of these its plasticity based on actual biophysical reactions in the empirical models is that they do not explain the synapse. Presynaptic stimuli lead to the release of glutamate biomolecular mechanisms underlying STDP at a cellular neurotransmitter, which is illustrated by the module level. Glutamate Receptor. Postsynaptic activation leads to the In contrast, mechanistic models of synaptic plasticity [4]- propagation of the dendritic action potential in NMDA [6] based on biophysical mechanisms at the molecular level channel. Calcium signaling reaction begins when NMDA are more informative in interpreting experimental findings. receptors promote calcium influx, which is enabled by a Starting from the calcium control hypothesis [4] which glutamate influx and prolonged membrane depolarization supports the well-known Bienenstock-Cooper-Munro due to the back propagating dendritic action potential. This (BCM) rule [7], these mechanistic models suggest that function is described in model Calcium Integrator. The final repetitive postsynaptic NMDA receptor activation allowing EPSC Transduction module constructs the balance between an influx of calcium ions is the trigger for activity- the kinase and the phosphatase, which is determined by the dependent synaptic plasticity. These receptors also serve as total amount of calcium flowing to the postsynaptic membrane. This work was supported by NIH grants EB005460, RR028241 and Our design chooses current mode circuit based on iono- HL067966 and sponsored by the DARPA MIT-LL Advanced Microsystems neuromorphic modeling with ion channel details [9], which Technology Core Program under Air Force Contract F19628-00-C-0002. is different from silicon neurons in other neuromorphic Yicong Meng, Joshua J. C. Monzon, and Chi-Sang Poon are with models with only limited ion channel descriptions. The rest Massachusetts Institute of Technology, Cambridge, MA 02139 (e-mails: [email protected], [email protected]). of this section describes the circuit blocks in details. Kuan Zhou is with The University of New Hampshire, NH 03824. 978-1-4244-4122-8/11/$26.00 ©2011 IEEE 7274 g Glu Glutamate Receptor K NMDAmax glu gNMDA V dent ,Glu = (3) 1+exp kNMDA V 1/2 -V dent Glu+Kglu Glutamate Glutamate Vglu Voltage to Iglu Reaction The second term in Eq. (3) demonstrates the glutamate Current Circuit Converter receptor dependence and has been implemented as Iglunorm in Iglunorm BCM Eq. (2). The first term is in complicated sigmoid format and Calcium Integrator constants NMDA Channel seems challenging for aVLSI implementation. However, by Glue and Vdent gNMDA Total Calcium Catotal BCM based Ca dependent Generation to delta EPSC studying the I-V characteristic of the differential pair, it is V1/2 NMDA channel Circuit Converter found that its I-V curve was quite similar to the NMDA Vdent EPSC channel conductance dynamics, Ident Dendritic 1 Voltage to IIout bias (4) EPSC VV Current WL/ Converter Transduction 1 11e t WL22/ Figure 1: Block diagram for aVLSI synapse By comparing Eq. (3) and (4), the NMDA channel conductance parameters can be easily mapped into the A. Glutamate Receptor aVLSI differential pair. Ibias is replaced by Iglunorm and V+, V− It is shown that NMDA receptor-gated ion channels are are mapped to V1/2, Vdent. The two MOSFETs of the the main pathways for calcium flux to the postsynaptic differential pair should have exactly the same size. neuron [10][11]. To open the NMDA-receptor channels, it requires both the binding of glutamate and a substantial C. Calcium Integrator degree of depolarization. Glutamate binding can be Once we have obtained NMDA channel conductance, we described by the ligand-receptor model, where glutamate can determine the amount of calcium flowing through our ligand concentration combines glutamate receptors in the synapse to the postsynaptic neuron. As the NMDA receptors postsynaptic membrane with an association constant of Kglu. are the major gateway of calcium inflow, calcium Ultimately at equilibrium, the ratio of bound glutamate to concentration is proportional to the integration of current the total glutamate concentration is given by flow through NMDA receptors over the time span of stimuli, Glu Ca INMDA dt g NMDA V dent dt (5) (1) ttstimuli stimuli Glu+Kglu The ratio above is a simple arithmetic representation that Here the NMDA current INMDA is the product of NMDA involves addition and division. Using aVLSI circuitry, we conductance and dendrite membrane potential. could implement this with a current adder and a current The multiplication between two signals gNMDA and Vdent can be negative because Vdent can be a biphasic signal. divider. However, since the presynaptic input Vglu is a voltage signal, it has to be first converted to current signal Therefore, a four quadrant multiplier is designed to by using a wide linear range transconductance amplifier implement the multiplication in Eq. (5), as shown in Figure 2(c) and (d). The implementation of integration in circuit is (TCA). Since Iglu is used twice in the equation, it was trivial as it could be easily achieved by charging a capacitor mirrored twice and a constant current Kglu is added to one of the mirrored path. A translinear current divider is used to with calcium flow. divide the two mirrored currents to obtain the maximum D. EPSC Transduction NMDA receptor conductance. The transfer function can be Accumulated calcium in the postsynaptic compartment given by through the action of NMDA receptors strongly influences kINMDAmax I glu the action of synaptic plasticity. Depending upon the total I=glunorm (2) Iglu +K glu amount of calcium inflow, postsynaptic calcium can either upregulate or downregulate the signal transduction pathways where k and INMDAmax are constant gain factors. Figure 2(a) demonstrates the schematic circuit we have developed for that lead to synaptic plasticity. This influence can be the Glutamate receptor. The current sink out of the divider is achieved in two steps. The calcium binds with calcium- mirrored to be a current source so that it connects seamlessly dependent protein kinase or phosphatase. These enzyme- with the next current block. calcium complexes either insert active AMPA receptors [12] from the membrane under kinase or remove AMPA B. NMDA Channel