🧠 Module 3 · From Biology to Algorithm · Chapter 3.2 · 14 min read

The Synapse

10¹⁴ connections, a 10 nm gap — the brain's real compute engine.

Prerequisites

3.1 — Neuron Biology

What you'll learn here

Name the parts of a synapse (pre-, cleft, post-) and describe what each does
Explain why chemical synapses dominate over electrical ones
Write the EPSP/IPSP linear-sum equation ($V = \sum w_i \cdot s_i$)
Connect LTP/LTD to the molecular cascade that updates the weight
Compare per-event synaptic energy with SIDRA memristor SET energy

Hook: A 10-Nanometer Compute Engine

A neuron alone is just a comparator (chapter 3.1). The actual computation happens at the connection — at the synapse.

The numbers are dramatic: the human brain holds ~10¹⁴ to 10¹⁵ synapses. Each synapse is a 10-20 nm gap (the synaptic cleft). Comparison:

Brain: 10¹⁴ synapses × 10 nm cleft → total “compute surface” ~10⁵ µm²
SIDRA Y1: 419M memristors × 100 nm cell → total ~4×10⁹ nm² = 4×10³ µm²

The brain’s synaptic surface is roughly 25× SIDRA Y1’s, but each synapse is far smaller and uses far less energy. A single synaptic event consumes ~10 fJ (10⁻¹⁴ J); a SIDRA SET consumes ~10 pJ (10⁻¹¹ J). A factor of 1000.

This chapter covers the physics, chemistry, and plasticity of the synapse — and shows why the HfO₂ memristor is mathematically the right choice to imitate it.

Intuition: Three Parts, One Signal Hop

A chemical synapse has three parts:

Part	Where	Contents
Pre-synaptic terminal	Axon end	Vesicles (full of neurotransmitter), Ca²⁺ channels
Synaptic cleft	Between cells	10-20 nm gap, intercellular fluid
Post-synaptic membrane	Dendritic spine	Receptors (AMPA, NMDA, GABA-A)

Signal hop:

Spike arrives at the axon terminal → membrane depolarizes.
Voltage-gated Ca²⁺ channels open → Ca²⁺ pours in.
Ca²⁺ triggers vesicle fusion with the presynaptic membrane.
Vesicle contents (thousands of neurotransmitter molecules) spill into the cleft.
Neurotransmitter binds receptors on the other side → ion channels open.
The postsynaptic membrane depolarizes (EPSP) or hyperpolarizes (IPSP).

Key numbers: one spike → ~1 vesicle release (probabilistic, typical p = 0.1-0.9). One vesicle → ~5000 neurotransmitter molecules → ~10-50 pA postsynaptic current pulse (~1-5 ms).

Chemical vs electrical synapse:

Chemical (dominant, ~99%): slow (0.5-2 ms delay), gain-tunable, plastic.
Electrical (gap junction): fast (no delay), bidirectional, fixed gain. Used in synchronization circuits.

Synapse = a tunable, gain-controlled signal switch. The weight ( $w$ ) = receptor count × neurotransmitter amount × postsynaptic resistance. Those three factors together set $w$ . SIDRA’s memristor conductance $G$ is the analog of $w$ .

Formalism: EPSP, IPSP, Synaptic Summation

L1 · Başlangıç

A single synaptic event changes the post-membrane voltage in an alpha-function shape:

\text{EPSP}(t) = w \cdot \frac{t}{\tau_s} e^{1 - t/\tau_s}

$w$ — synaptic weight (peak height in mV)
$\tau_s$ — synaptic time constant (~5 ms AMPA, ~50 ms NMDA)

EPSP peaks ~ $\tau_s$ after the spike; decays back to zero in ~3 $\tau_s$ .

Total membrane voltage:

V_m(t) = V_{\text{rest}} + \sum_i w_i \cdot s_i(t - t_i)

$w_i$ — weight of synapse $i$ (positive for excitatory, negative for inhibitory)
$s_i$ — alpha-shaped synaptic function
$t_i$ — arrival time of the i-th spike

This is linear summation — biology approximates it well for small EPSPs. With ~20+ synapses simultaneously triggered, the neuron crosses threshold.

L2 · Tam

Receptor types and dynamics:

Receptor	Neurotransmitter	Time constant	Role
AMPA	Glutamate	1-5 ms	Fast excitation, the main signal path
NMDA	Glutamate (+ Mg²⁺ block)	50-150 ms	Slow, voltage-dependent, coincidence detector
GABA-A	GABA	5-20 ms	Fast inhibition (Cl⁻ flux)
GABA-B	GABA	100-500 ms	Slow inhibition (K⁺ channel)

NMDA’s special role — coincidence detection:

NMDA opens only when both are true:

Glutamate is bound (presynaptic active)
The postsynaptic membrane is depolarized (Mg²⁺ block lifted)

So pre + post simultaneously active opens NMDA → Ca²⁺ flows → synaptic plasticity is triggered. This is the biological mechanism of Hebb’s rule (“cells that fire together wire together”).

EPSP/IPSP magnitudes:

Single AMPA EPSP: ~0.1-1 mV postsynaptic peak.
EPSP needed for threshold: ~15 mV (−70 → −55).
So a neuron needs 15-150 simultaneous synaptic events to fire. A typical cortical neuron has 1000-10000 synapses → even a small fraction firing is enough.

Synaptic delay budget:

Axon conduction: 0.1-100 m/s, average ~1 m/s → 1 mm = 1 ms.
Synaptic delay: 0.5-2 ms.
Postsynaptic integration: 5-20 ms (τ_m).
Total ~5-25 ms from one synapse to the next. That’s the brain’s “thinking” timescale.

L3 · Derin

Plasticity — synaptic weight change:

Two main directions:

LTP (Long-Term Potentiation): $w$ increases. High-frequency pre+post activity triggers it. AMPA receptor count rises.
LTD (Long-Term Depression): $w$ decreases. Low-frequency or mistimed activity triggers it. AMPA receptors are internalized.

Molecular cascade (simplified):

Ca²⁺ flows in through NMDA.
High and brief Ca²⁺ → CaMKII activates → AMPA phosphorylates + inserts → LTP.
Low and prolonged Ca²⁺ → calcineurin activates → AMPA dephosphorylates + endocytoses → LTD.

The Ca²⁺ magnitude flips the sign — that’s the biological basis of BCM theory (Bienenstock-Cooper-Munro 1982).

Spike-timing-dependent plasticity (STDP):

Bi & Poo (1998) experiment: pre→post within 20 ms gives LTP; post→pre within 20 ms gives LTD. Asymmetric learning window. Detail in chapter 3.8.

Memristor parallel (bridge to 3.7):

Synapse	Memristor
Weight $w$ (AMPA receptor count)	Conductance $G$ (filament thickness)
LTP (AMPA insertion)	SET (grow filament)
LTD (AMPA endocytosis)	RESET (break filament)
EPSP (presynaptic spike → postsynaptic current)	Voltage pulse → current pulse
Synaptic info: ~4-6 bits (256 discrete $w$ levels)	SIDRA: 256 levels = 8 bit analog

This isn’t coincidence — HfO₂ filament dynamics share the same math as synaptic plasticity, on a different substrate.

Experiment: 1000 Synapses, Push the Neuron to Threshold

A cortical pyramidal neuron has 5000 synapses, each EPSP peaking at 0.5 mV. How many simultaneous synaptic events does it take to cross threshold (~15 mV depolarization)?

Step 1 — linear estimate: 15 mV / 0.5 mV = 30 simultaneous synapses (0.6% activity).

Step 2 — realistic (no NMDA): linear approx is good below threshold; saturation kicks in near threshold. In practice ~50 EPSPs may be needed → ~1% activity.

Step 3 — what cortical sparsity? Average cortical activity is ~1-3% → which neurons are above threshold shifts continuously. The brain runs on sparse coding.

Step 4 — energy:

30 synaptic events × 10 fJ = 0.3 pJ for the post-neuron integration.
Then 1 spike (~0.3 nJ) leaves.
Synapse cost / spike cost = 0.3 pJ / 0.3 nJ = 1/1000. Spikes are expensive, synapses are cheap.

SIDRA parallel: a crossbar column reads 256 memristors in parallel (each ~0.1 pJ) → 25.6 pJ total. Instead of a spike, a “column current” emerges — the analog of the brain’s synaptic integration.

Quick Quiz

1/6What is the first trigger for signal transmission at a chemical synapse?

Lab Exercise

How many real synapses does SIDRA Y1’s 419M memristors actually replace?

Data:

Memristor levels: 256 (8 bit)
Synaptic information content (estimates): ~4-6 bit (16-64 discrete weight levels)
Brain synapse count: 1.5 × 10¹⁴
SIDRA Y1: 419M = 4.19 × 10⁸ memristors
Per-synaptic-event energy: ~10 fJ
Per-memristor read energy: ~0.1 pJ

Questions:

(a) Information per SIDRA cell (bits)? Ratio to per-synapse information? (b) Y1 total information capacity (bits) vs brain? Percentage? (c) Y1 read energy how much above synapse? (d) Y100 target 100 billion memristors. What fraction of brain synapse count? (e) “Energy per bit” for Y1 vs synapse vs Y100?

Solutions

(a) SIDRA: log₂(256) = 8 bit/cell. Synapse: ~5 bit. Ratio: 8/5 = 1.6× — one SIDRA cell carries more bits than one synapse (analog advantage).

(b) Y1: 4.19×10⁸ × 8 = 3.35 × 10⁹ bit ≈ 0.42 GB. Brain: 1.5×10¹⁴ × 5 = 7.5 × 10¹⁴ bit ≈ 94 TB. Ratio: 0.42 GB / 94 TB ≈ 4.5 × 10⁻⁶ ≈ 4 parts per million.

(c) 0.1 pJ / 10 fJ = 10×. SIDRA spends ~10× more per read than a synapse spends per event. But SIDRA reads 8 bit, synapse fires ~5 bit → per bit: 0.1pJ/8bit = 12.5 fJ/bit vs 10fJ/5bit = 2 fJ/bit. Synapse is ~6× better per bit. Memristors are closer to their physical floor than synapses.

(d) Y100: 10¹¹ / 1.5×10¹⁴ = 0.067% ≈ ~0.07%. Still not full brain scale, but the order of “a meaningful cortical area”.

(e) Y1: ~12.5 fJ/bit read. Synapse: ~2 fJ/bit. Y100 target: drive memristor SET from 1 pJ to 0.1 pJ (new materials, smaller cell). ~1.25 fJ/bit — on par with synapses. That’s the real Y100 goal.

Cheat Sheet

Synapse 3 parts: pre-terminal (vesicles + Ca²⁺), cleft (10-20 nm), post-membrane (receptors).
Signal flow: spike → Ca²⁺ → vesicle → neurotransmitter → receptor → postsynaptic current.
Receptors: AMPA (fast excitatory, 5 ms), NMDA (slow, coincidence, 100 ms), GABA (inhibitory).
EPSP summation: $V = V_{\text{rest}} + \sum w_i \cdot s_i$ (approximately linear). Threshold needs ~30 events.
Plasticity: LTP (Ca²⁺ ↑ → AMPA insertion → w ↑), LTD (Ca²⁺ ↓ prolonged → AMPA endocytosis → w ↓).
Synaptic info: ~5 bit/synapse, ~10 fJ/event, ~10¹⁴ total in brain.
Memristor mapping: $w \leftrightarrow G$ , LTP ↔ SET, LTD ↔ RESET. SIDRA: 256 levels = 8 bit.

Vision: Synapse-Memristor Hybrid and Bio-Compatible Chips

The synapse is the most efficient tunable connection nature has ever produced. SIDRA’s roadmap competes with that efficiency:

Y1 (today): HfO₂ memristor = inorganic analog synapse. 8 bit (256 levels), 10 pJ SET, 0.1 pJ read. ~6× behind synapse on bit-per-energy.
Y3 (2027): HfAlO doping → 10 bit (1024 levels), better retention. ~3× behind.
Y10 (2029): hybrid HfO₂ + ferroelectric HZO. 12 bit, 1 pJ SET. ~1.5× behind.
Y100 (2031+): new materials (CNT-reinforced oxide or 2D heterostructure). 16 bit analog, ~0.1 pJ SET. Matches synaptic efficiency.
Y1000 (long horizon): Organic synapse (PEDOT:PSS, neurotransmitter-coupled receptor analogs). Implantable into the brain. SIDRA’s bio-compatible generation.

Strategic opportunity for Türkiye: organic synapse + memristor crossover is a category outside the classical silicon fab race. Polymer chemistry, ALD infrastructure, and workshop discipline together can stand up a world-leading organic neuromorphic fab in Türkiye. This is one of the SIDRA workshop’s long-horizon founding visions.

Unexpected future: a hybrid carbon-silicon neuron. A single biological neuron + 1000 SIDRA memristor synapses → a “semi-living” compute unit. Sci-fi today, lab prototype within 15-20 years.

Prerequisites

What you'll learn here

🪝 Hook: A 10-Nanometer Compute Engine

🧭 Intuition: Three Parts, One Signal Hop

📐 Formalism: EPSP, IPSP, Synaptic Summation

🧪 Experiment: 1000 Synapses, Push the Neuron to Threshold

📝 Quick Quiz

🛠️ Lab Exercise

🗂️ Cheat Sheet

🔮 Vision: Synapse-Memristor Hybrid and Bio-Compatible Chips

📚 Further Reading