708 lines
28 KiB
Markdown
708 lines
28 KiB
Markdown
# **Detailed Temporal Dynamics of Presynaptic Neurotransmitter Release**
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*With concentration changes, calcium clearance mechanisms, and multi-timescale modifications of release probability (Pr)*
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---
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## **Baseline State (Resting Condition)**
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**Time:** Continuous resting state
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**Presynaptic [Ca²⁺]:** ~100 nM (resting cytosolic concentration)
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**Pr baseline:** 0.3 (30% release probability per action potential)
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**Ready vesicles:** 5-10 vesicles in readily releasable pool (RRP)
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**ATP/GTP levels:** Normal
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**Phosphorylation state:** Baseline kinase/phosphatase balance
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---
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## **PHASE 1: FAST TIMESCALE (0-100 ms) - SINGLE SPIKE CYCLE**
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### **0.0-0.5 ms: Action Potential Arrival & Calcium Influx**
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```
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AP depolarization (+30mV) reaches terminal
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↓
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VGCCs (P/Q-type) open with ~50% probability
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↓
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Ca²⁺ enters through ~20 channels per active zone
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↓
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**Local [Ca²⁺] at release site: 100 nM → 10-50 µM** (peak in nanodomain)
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↓
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Calcium diffuses ~20-30 nm to docked vesicles
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↓
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**PROBABILISTIC DECISION POINT:**
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Time window for decision: ~0.2-0.5 ms
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```
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### **0.5-2.0 ms: Release Decision & Execution**
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```
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├── **PATH A: RELEASE OCCURS (Pr = 0.3)**
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│ ↓
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│ [Ca²⁺] at Synaptotagmin > 10 µM
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│ ↓
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│ 3-5 Ca²⁺ ions bind to C2 domains of Synaptotagmin-1
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│ ↓
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│ Synaptotagmin inserts into membrane (Kd ~5-10 µM)
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│ ↓
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│ **SNARE complex completes zippering** (t ≈ 0.8 ms)
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│ ↓
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│ Fusion pore opens (diameter ~1 nm initially)
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│ ↓
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│ **~5000 glutamate molecules released** (t = 1-2 ms)
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│ ↓
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│ Fusion pore expands → full fusion
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│ ↓
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│ Vesicle membrane incorporated into plasma membrane
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│
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└── **PATH B: NO RELEASE (1-Pr = 0.7)**
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↓
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[Ca²⁺] at Synaptotagmin < 5 µM (insufficient binding)
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↓
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Calcium buffers (calbindin, parvalbumin) bind Ca²⁺
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↓
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Vesicle remains docked/primed
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↓
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No fusion → **silent spike**
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```
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### **2.0-50 ms: Calcium Clearance & Fast Recovery**
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```
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**Primary clearance mechanisms:**
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1. Plasma Membrane Ca²⁺ ATPase (PMCA):
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- Kd ~100-200 nM
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- Rate: 30 Ca²⁺/sec per pump
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- **Clears 90% of Ca²⁺ in 10-20 ms**
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2. Na⁺/Ca²⁺ exchanger (NCX):
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- Lower affinity (Kd ~1 µM) but higher capacity
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- Important for bulk clearance
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3. Mitochondrial uptake:
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- MCU (mitochondrial Ca²⁺ uniporter)
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- Kd ~10-20 µM
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- Slower but provides long-term buffering
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4. Endoplasmic reticulum uptake (SERCA):
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- Sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase
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- Kd ~0.5 µM
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**Result:** [Ca²⁺] returns to ~500 nM by 50 ms
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**Residual [Ca²⁺]:** ~200-300 nM persists for 100-500 ms
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**Vesicle retrieval:** Clathrin-mediated endocytosis begins at ~1 sec
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```
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---
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## **PHASE 2: SHORT-TERM PLASTICITY (100 ms - 10 sec)**
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### **Example: Spike Train at 50 Hz (20 ms interval)**
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```
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Spike 1: Pr = 0.3 → Release probability
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Spike 2 (20 ms later):
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Residual [Ca²⁺] = 300 nM
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Pr increases to 0.45 (facilitation)
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Ca²⁺ influx adds to residual Ca²⁺
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Spike 3 (40 ms):
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Residual [Ca²⁺] accumulates to 400 nM
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Pr = 0.55
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But RRP depletion begins (STD component)
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Spike 4 (60 ms):
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RRP depleted to 60%
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Effective Pr = 0.5 × 0.6 = 0.3 (balance facilitation/depletion)
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Spike 5-10:
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Steady-state: Pr ~0.25, RRP ~40% of baseline
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```
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### **Molecular Mechanisms of Short-Term Changes:**
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```
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**Facilitation (0-500 ms):**
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Residual Ca²⁺ (~200-500 nM) → binds to Calmodulin
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↓
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Ca²⁺-Calmodulin binds to Munc13
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↓
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Munc13 increases priming rate 3-5×
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↓
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**Pr increases for next spike**
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**Depression (0-2 sec):**
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Vesicle fusion → RRP depletion
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↓
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Recovery requires:
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1. Vesicle recycling (endocytosis: 1-10 sec)
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2. Vesicle repriming (2-30 sec)
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3. Reserve pool mobilization (seconds)
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```
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---
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## **PHASE 3: MEDIUM-TERM ADAPTATION (10 sec - 10 min)**
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### **Example: LTP Induction at 100 Hz for 1 sec (Tetanus)**
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```
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**0-1 sec: High-frequency stimulation**
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- 100 APs delivered
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- Massive Ca²⁺ accumulation in terminal
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- [Ca²⁺] builds to sustained 1-2 µM
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- Complete RRP depletion
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- Strong glutamate release
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**1-30 sec: Retrograde signaling arrives**
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Postsynaptic spine produces:
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1. Nitric Oxide (NO) - diffuses in seconds
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2. Brain-Derived Neurotrophic Factor (BDNF) - released in minutes
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3. Endocannabinoids (eCBs) - for LTD case
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NO diffuses into presynaptic terminal (t ≈ 5-10 sec)
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↓
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**NO activates soluble guanylyl cyclase (sGC)**
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↓
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sGC produces cGMP from GTP
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↓
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**cGMP increases from ~1 nM to 100 nM**
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↓
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cGMP activates Protein Kinase G (PKG)
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```
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### **30 sec - 5 min: PKG-Mediated Pr Enhancement**
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```
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PKG phosphorylates multiple targets:
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1. **VGCCs (P/Q-type):**
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- Phosphorylation at specific serine residues
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- Open probability increases from 0.5 → 0.7
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- More Ca²⁺ enters per AP
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2. **Munc18:**
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- Enhanced interaction with Syntaxin
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- Vesicle priming rate increases 2×
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3. **Synaptotagmin-1:**
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- Increased Ca²⁺ sensitivity (Kd decreases from 10→5 µM)
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- Faster binding kinetics
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4. **RIM proteins:**
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- Enhanced vesicle tethering
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- Better VGCC-vesicle coupling
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**Net effect by 5 min:**
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- Pr increases from 0.3 → 0.5
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- Baseline Ca²⁺ sensitivity increased
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- Readily Releasable Pool size increases 30%
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```
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---
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## **PHASE 4: SLOW CONSOLIDATION (10 min - 2 hours)**
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### **Local Protein Synthesis (Presynaptic)**
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```
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**30 min - 2 hours:**
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BDNF binds to TrkB receptors on presynaptic terminal
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↓
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Activation of PI3K/mTOR pathway
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↓
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**Local translation of presynaptic mRNAs:**
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1. VGCC subunits (α1A, β4)
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2. Synaptotagmin-1
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3. Munc13-1
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4. SNARE proteins
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**Result by 2 hours:**
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- 50% more VGCCs clustered at active zone
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- 40% more Synaptotagmin molecules per vesicle
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- Pr stabilizes at 0.6
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```
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### **Metabolic Support System**
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```
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**Astrocyte coordination:**
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1. Glutamate uptake → converted to glutamine
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2. Glutamine exported to presynaptic terminal
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3. Presynaptic mitochondria increase oxidative phosphorylation
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4. ATP production increases 2× to support enhanced release
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**Energy requirements:**
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- Vesicle recycling: ~10,000 ATP/vesicle
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- Ca²⁺ clearance: ~1 ATP/2 Ca²⁺ ions
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- Protein synthesis: ~4 ATP/amino acid
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```
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---
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## **PHASE 5: STRUCTURAL CONSOLIDATION (2 hours - 24 hours)**
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### **Nuclear Signaling & Gene Expression**
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```
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**2-6 hours:**
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Persistent kinase activity (PKG, PKA, MAPK)
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↓
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CREB phosphorylation in presynaptic nucleus
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↓
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**Gene expression changes:**
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1. Structural proteins (Bassoon, Piccolo)
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2. Active zone components
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3. Vesicle cycle proteins
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4. Metabolic enzymes
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**12-24 hours:**
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New proteins arrive via axonal transport
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↓
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**Active zone remodeling:**
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- Active zone area increases 30-50%
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- More docked vesicles (RRP size doubles)
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- VGCC-vesicle distance decreases to 15 nm
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- **Pr stabilizes at 0.7-0.8**
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```
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---
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## **CALCIUM HOMEOSTASIS TIMELINE SUMMARY**
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| Time | \[Ca²⁺\] at Release Site | Clearance Mechanism | Residual Effect |
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|--------|--------------------------|--------------------------|----------------------------|
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| 0 ms | 100 nM (baseline) | \- | \- |
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| 0.5 ms | 10-50 µM (peak) | Diffusion only | Fusion decision |
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| 5 ms | 1-5 µM | Fast buffers (calbindin) | Ca²⁺-calmodulin activation |
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| 20 ms | 500 nM | PMCA pumps active | Facilitation of next spike |
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| 100 ms | 300 nM | NCX contributes | Augmentation phase |
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| 1 sec | 200 nM | Mitochondrial uptake | Potentiation |
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| 10 sec | 150 nM | Steady-state clearance | LTP induction possible |
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| 1 min | 120 nM | Full homeostasis | \- |
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| 1 hour | 100 nM | Normal resting state | \- |
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---
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## **EXAMPLE: COMPLETE LTP TIMELINE**
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### **Day 1: Induction Phase**
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```
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**T=0:** 100 Hz tetanus (1 sec)
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**T=5 sec:** NO arrives at presynaptic terminal
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**T=30 sec:** cGMP peaks, PKG activated
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**T=5 min:** Pr increases to 0.45 (phosphorylation)
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**T=30 min:** Local protein synthesis begins
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**T=2 hours:** Pr = 0.55, structural proteins arriving
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**T=6 hours:** Active zone remodeling begins
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**T=24 hours:** Pr stabilizes at 0.65, active zone enlarged 40%
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```
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### **Day 2-7: Maintenance**
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```
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**Metabolic support ongoing:**
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- Astrocyte supplies glutamine/lactate
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- Mitochondrial density increases near active zone
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- Vesicle recycling efficiency improves
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**Structural stabilization:**
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- New active zone material incorporated
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- Cytoskeleton reorganizes
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- Pr maintains at 0.65-0.70
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```
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---
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## **KEY BIOLOGICAL INSIGHTS**
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1. **Pr is multi-dimensional:**
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- **Fast component:** Vesicle availability × Ca²⁺ sensitivity
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- **Slow component:** Protein composition × active zone geometry
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2. **Energy dependence:**
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- Ca²⁺ clearance requires constant ATP
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- Without ATP, [Ca²⁺] remains elevated → toxicity
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- Metabolic veto: Low ATP → release inhibition despite Ca²⁺
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3. **Timescale hierarchy:**
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- **ms:** Existing protein modification (phosphorylation)
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- **min:** Local protein synthesis
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- **hours:** Nuclear transcription
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- **days:** Structural reorganization
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4. **Homeostatic balance:**
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- Enhanced Pr increases metabolic demand
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- Requires coordinated astrocyte support
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- Long-term maintenance depends on energy availability
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This detailed timeline shows how a single probabilistic event (vesicle release) is embedded in a complex, multi-timescale regulatory system that balances immediate communication needs with long-term information storage and metabolic sustainability.
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---
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---
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---
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Based on the provided document, here is a specification of the Short-Term Plasticity (STP/STD) and Long-Term Plasticity (LTP/LTD) mechanisms between the Presynapse and Postsynapse, detailing both internal processes and their interactions, with explicit timescales.
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### **Summary: Primary Plasticity Mechanisms & Timescales**
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| Mechanism | Primary Locus | Key Internal Trigger | Key Interactive Signal | Timescale | Functional Role |
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|-----------------------------------|------------------|-----------------------------------------------|-------------------------------------------------|------------------------------------|------------------------------------------------------------|
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| **Short-Term Depression (STD)** | **Presynaptic** | Vesicle pool depletion | Reduced glutamate release | **Fast (<100ms)** | Filters high-frequency bursts; transient synaptic fatigue. |
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| **Short-Term Potentiation (STP)** | **Presynaptic** | Residual Ca²⁺ buildup | Increased glutamate release probability ($P_r$) | **Fast to Medium (<100ms to 10s)** | Facilitates temporal summation; augments recent activity. |
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| **Long-Term Depression (LTD)** | **Postsynaptic** | Moderate, sustained Ca²⁺ influx (~1-5 µM) | Retrograde endocannabinoids (eCBs) | **Slow (Seconds to Minutes)** | Weakens ineffective connections; homeostatic adjustment. |
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| **Long-Term Potentiation (LTP)** | **Postsynaptic** | Strong, coincident Ca²⁺ influx (>10 µM) | Retrograde NO/BDNF | **Slow (Seconds to Minutes)** | Strengthens correlated pre- and postsynaptic activity. |
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| **Structural LTP/LTD** | **Both** | Persistent molecular tags & protein synthesis | Trophic factors & homeostatic scaling | **Structural (Days+)** | Embeds memory persistently via physical changes. |
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---
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### **Detailed Breakdown by Timescale**
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#### **1. Fast Timescale (<100 ms): STP & STD Internal Mechanisms**
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* **Presynaptic Internal (STD):** Rapid vesicle fusion and release depletes the readily releasable pool. This is a **presynaptic, internal** mechanism causing a transient decrease in synaptic strength.
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* **Presynaptic Internal (STP):** Residual Ca²⁺ from a preceding action potential lingers, increasing the release probability ($P_r$) for the next spike. This is a **presynaptic, internal** facilitatory mechanism.
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* **Interaction (Fast Signaling):** The presynapse releases **glutamate** (outgoing signal). The postsynapse receives it and, if sufficiently depolarized, opens NMDA receptors, allowing a **Ca²⁺ influx**. This **Ca²⁺ transient** is the **postsynaptic, internal** coincidence detector signal that initiates the cascade for slower plasticity.
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#### **2. Medium Timescale (100 ms – 10 s): Augmentation & Modulation**
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* **Presynaptic Internal:** Augmentation via Munc13 proteins modifies $P_r$ based on Ca²⁺ sensing. This is a **presynaptic, internal** continuation of STP.
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* **Postsynaptic Internal:** Metabotropic glutamate receptor (mGluR) activation modulates local spine excitability and prepares plasticity pathways. This is a **postsynaptic, internal** modulatory state.
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* **Interaction:** Largely an extension of fast signaling, setting the stage for slower decisions. The **pattern of glutamate release** interacts with the **postsynaptic voltage state**.
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#### **3. Slow Timescale (Seconds – Minutes): LTP & LTD Decision & Expression**
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This is the critical window for **bidirectional interaction** that establishes long-term change.
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* **Postsynaptic Internal (The Decision):**
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* **LTP Trigger:** **High, localized Ca²⁺** (from strong NMDA activation + back-propagating AP) activates **CaMKII**, creating a **plasticity tag**.
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* **LTD Trigger:** **Moderate, sustained Ca²⁺** (from isolated glutamate release or low-frequency stimulation) activates phosphatases (e.g., calcineurin).
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* This decision is **postsynaptic and internal**.
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* **Interaction (Retrograde Messaging):**
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* For **LTP:** The postsynapse synthesizes and releases **retrograde signals (NO, BDNF)**. These diffuse to the presynapse.
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* For **LTD:** The postsynapse releases **endocannabinoids (eCBs)**.
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* These are **interactive signals from postsynapse to presynapse**.
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* **Presynaptic Internal (Expression):**
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* **For LTP:** NO/BDNF activate enzymatic cascades that **persistently increase the baseline** $P_r$.
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* **For LTD:** eCBs bind to CB1 receptors, inhibiting VGCCs and **persistently decreasing** $P_r$ (Direct Synaptic Depression, DSE).
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* This change in baseline $P_r$ is the **presynaptic, internal** expression of the long-term change.
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#### **4. Metabolic Timescale (Minutes – Hours): Consolidation**
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* **Interaction (Astrocyte Bridge):** The astrocyte supplies **D-serine** (co-agonist for NMDAR) and **lactate** (energy). This **external, interactive support** is required for stable consolidation.
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* **Postsynaptic Internal:** The spine initiates **local protein synthesis**, using the "tag" to capture newly made proteins, transitioning early-LTP/LTD to a more stable state. This is a **postsynaptic, internal** consolidation process.
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#### **5. Structural Timescale (Days+): Embodiment**
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* **Presynaptic Internal:** The bouton **grows or retracts**, changing the active zone size and vesicle pool. This is a **presynaptic, internal** structural change.
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* **Postsynaptic Internal:** The spine **changes its volume and number of AMPA receptor slots**. This is a **postsynaptic, internal** structural change.
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* **Interaction (Global Scaling):** The soma sends **homeostatic scaling signals** to all synapses (including this one) to maintain network stability, providing a **top-down, interactive modulation** that can override local weights.
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### **Conclusion**
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* **STP/STD** are predominantly **presynaptic, internal** phenomena operating on **fast to medium timescales** (ms to s), governed by vesicle dynamics and residual calcium.
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* **LTP/LTD** are initiated by a **postsynaptic, internal** calcium-based decision on a **slow timescale** (s to min). Their expression involves a **critical bidirectional interaction**: retrograde signals (NO/BDNF for LTP, eCBs for LTD) from the postsynapse induce **presynaptic, internal** changes in baseline $P_r$.
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* These changes are then stabilized on **metabolic and structural timescales** through astrocytic support and physical remodeling of both synaptic components, embedding the memory trace in the physical architecture of the connection.
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---
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---
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---
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**In biology, presynaptic release probability (Pr) emerges from a dynamic molecular machine, not a simple number.** Changing Pr involves coordinated modifications to multiple components of the vesicle release apparatus. Here's the biological process breakdown:
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## **The Pr Machinery: Three Core Components**
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Pr = f(**Calcium Influx** × **Vesicle Readiness** × **Fusion Machinery Sensitivity**)
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### **1. Modulating Calcium Influx**
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**Target:** Voltage-Gated Calcium Channels (VGCCs, mainly P/Q and N-type).
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- **Increasing Pr:** Phosphorylation of VGCCs by kinases (PKA, PKC) enhances their open probability or prolongs open time.
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- **Decreasing Pr:**
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- Direct inhibition by G-proteins (e.g., via activated CB1 receptors during LTD).
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- Physical relocation of channels away from release sites.
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- Dephosphorylation by phosphatases (calcineurin).
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**Biological Process:** A retrograde messenger (e.g., NO) activates a kinase cascade in the presynaptic terminal, leading to VGCC phosphorylation → more Ca²⁺ enters per action potential → higher Pr.
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### **2. Modulating Vesicle Readiness (Docking/Priming)**
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**Targets:** Docking proteins (Syntaxin, SNAP-25), priming proteins (Munc13, Munc18), and the vesicle pool itself.
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- **Increasing Pr:**
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- **Munc13 activation:** Residual Ca²⁺ binds to calmodulin, which binds to Munc13, increasing its priming activity. This is the main mechanism for **short-term facilitation**.
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- **Phosphorylation of priming proteins** by PKC/CaMKII makes them more active.
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- Increased expression or recruitment of vesicles to the "readily releasable pool" (RRP).
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- **Decreasing Pr:**
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- Dephosphorylation of priming proteins.
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- Physical depletion of RRP during high-frequency firing (STD).
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- Ubiquitination and degradation of priming proteins.
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### **3. Modulating Fusion Machinery Sensitivity (Ca²⁺ Sensor)**
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**Target:** The primary Ca²⁺ sensor Synaptotagmin and the SNARE complex (Syntaxin, Synaptobrevin, SNAP-25).
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- **Increasing Pr:**
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- Phosphorylation of Synaptotagmin increases its Ca²⁺ affinity.
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- Phosphorylation of SNARE proteins (e.g., SNAP-25 by PKC) enhances fusion kinetics.
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- Assembly of more SNARE complexes.
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- **Decreasing Pr:**
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- Cleavage of SNARE proteins by toxins (e.g., botulinum).
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- Increased binding of inhibitory proteins like Complexins.
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## **Specific Biological Pathways for Pr Changes**
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### **Fast Pr Increase (Facilitation, <100ms)**
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|
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**Process:** Action potential → Ca²⁺ influx → residual Ca²⁺ binds to calmodulin → Ca²⁺-calmodulin binds to Munc13 → Munc13 increases vesicle priming rate → more vesicles become release-ready for the next spike.
|
||
|
||
**Biological signature:** Transient, activity-dependent, decays with Ca²⁺ clearance.
|
||
|
||
### **Slow Pr Increase (LTP Expression, Minutes+)**
|
||
|
||
**Process:** Retrograde NO diffuses into presynaptic terminal → activates soluble guanylyl cyclase → produces cGMP → activates Protein Kinase G (PKG) → PKG phosphorylates multiple targets:
|
||
|
||
1. **VGCCs** → increased Ca²⁺ influx
|
||
2. **Munc18** → enhanced vesicle priming
|
||
3. **Synaptotagmin** → increased Ca²⁺ sensitivity **Plus:** Local protein synthesis of new vesicle proteins.
|
||
|
||
**Biological signature:** Persistent, requires gene expression for maintenance, structurally embedded.
|
||
|
||
### **Slow Pr Decrease (LTD Expression, Minutes+)**
|
||
|
||
**Process:** Retrograde eCBs bind presynaptic CB1 receptors → activates Gi/o proteins → βγ subunits directly inhibit VGCCs → reduced Ca²⁺ influx → decreased Pr.
|
||
**Additionally:** Gi/o inhibits adenylyl cyclase → reduced cAMP → reduced PKA activity → decreased phosphorylation of release machinery.
|
||
|
||
**Biological signature:** Reversible initially, can become structural with prolonged activation.
|
||
|
||
## **The Complete Biological Cascade for LTP-Induced Pr Increase**
|
||
|
||
```
|
||
Retrograde NO/BDNF
|
||
↓
|
||
Presynaptic receptor activation
|
||
↓
|
||
Second messenger cascade (cGMP/cAMP)
|
||
↓
|
||
Kinase activation (PKG/PKA/PKC)
|
||
↓
|
||
Phosphorylation of multiple targets:
|
||
1. VGCCs → ↑ Ca²⁺ influx per AP
|
||
2. Munc13/18 → ↑ vesicle priming rate
|
||
3. Synaptotagmin → ↑ Ca²⁺ sensitivity
|
||
4. SNARE proteins → ↑ fusion efficiency
|
||
↓
|
||
Increased Pr from baseline 0.2 → 0.4
|
||
↓
|
||
More reliable vesicle release per AP
|
||
↓
|
||
Structural reinforcement (Days+):
|
||
- More active zone material
|
||
- More docked vesicles
|
||
- Closer VGCC-vesicle coupling
|
||
```
|
||
|
||
## **Simulation vs. Biological Reality**
|
||
|
||
| In Simulation | In Biology |
|
||
|---------------------------------|-------------------------------------------------------------------------------------------------|
|
||
| `Pr = 0.3` | Pr emerges from: 5 docked vesicles × 40% channel open probability × 60% fusion probability |
|
||
| Update rule: `Pr += 0.1` if LTP | LTP: NO → cGMP → PKG → phosphorylates 3 proteins → increases Ca²⁺ influx 30% & priming rate 40% |
|
||
| Single variable | Distributed property of ~50 protein species |
|
||
| Instant change | Change occurs over: 100ms (fast), 1min (slow), 24hr (structural) |
|
||
|
||
## **Key Biological Insights**
|
||
|
||
1. **Pr is multi-parametric:** Not one number but the product of multiple probabilities.
|
||
2. **Redundancy:** Multiple pathways converge on Pr (kinases, protein synthesis, structural changes).
|
||
3. **Timescale hierarchy:**
|
||
- **Fast (ms):** Modify existing proteins (phosphorylation)
|
||
- **Slow (min):** Synthesize new proteins
|
||
- **Structural (days):** Change physical architecture
|
||
4. **Metabolic dependence:** All phosphorylation requires ATP. During energy crisis, kinases fail → Pr decreases even with "LTP signals."
|
||
5. **Cross-talk:** The same kinase (e.g., PKC) can phosphorylate both VGCCs and SNARE proteins, creating coordinated enhancement.
|
||
|
||
In essence, **Pr is the presynaptic terminal's "readiness state"**—a complex, dynamic equilibrium of dozens of interacting proteins that the neuron tunes through phosphorylation, gene expression, and structural remodeling to implement learning and adaptation.
|
||
|
||
---
|
||
|
||
---
|
||
|
||
---
|
||
|
||
**The presynapse does NOT release neurotransmitter every time a presynaptic spike arrives.** This is a fundamental principle of synaptic transmission: **release is probabilistic, not deterministic.**
|
||
|
||
## **What Pr Actually Influences**
|
||
|
||
**Pr (Release Probability)** determines the **likelihood** that a given action potential will trigger **vesicle fusion and neurotransmitter release**. It's essentially the synapse's **"coin toss" probability** for transmission.
|
||
|
||
### **Biological Reality:**
|
||
|
||
For a typical central synapse:
|
||
|
||
- **Pr ≈ 0.2-0.5** (meaning only 20-50% of spikes cause release)
|
||
- Some specialized synapses (like the neuromuscular junction) have Pr ≈ 0.9
|
||
- Some cortical synapses have Pr as low as 0.1
|
||
|
||
### **What Happens at a Presynaptic Terminal When a Spike Arrives:**
|
||
|
||
```
|
||
Action Potential arrives at terminal
|
||
↓
|
||
VGCCs open → Ca²⁺ enters
|
||
↓
|
||
**PROBABILISTIC DECISION POINT**
|
||
↓
|
||
├── **With probability Pr (e.g., 0.3):**
|
||
│ ↓
|
||
│ Ca²⁺ binds to Synaptotagmin on docked vesicle
|
||
│ ↓
|
||
│ SNARE complex zippers completely
|
||
│ ↓
|
||
│ Vesicle membrane fuses with presynaptic membrane
|
||
│ ↓
|
||
│ **GLUTAMATE RELEASED** → Postsynaptic response
|
||
│
|
||
└── **With probability 1-Pr (e.g., 0.7):**
|
||
↓
|
||
Ca²⁺ enters but insufficient to trigger fusion
|
||
↓
|
||
Vesicle remains docked but unfused
|
||
↓
|
||
**NO RELEASE** → No postsynaptic response
|
||
```
|
||
|
||
## **The Biological Basis of This Stochasticity**
|
||
|
||
### **1. Calcium Nanodomain Stochasticity**
|
||
|
||
- Ca²⁺ channels are ~20-30 nm from vesicle release sites
|
||
- When a channel opens, only ~100-300 Ca²⁺ ions enter
|
||
- These ions form a brief, localized "nanodomain"
|
||
- **Random diffusion and buffering** mean the Ca²⁺ concentration at the sensor varies randomly
|
||
- If <5-10 µM at the sensor → no fusion; if >10 µM → fusion
|
||
|
||
### **2. Molecular Stochasticity**
|
||
|
||
- **Synaptotagmin** (Ca²⁺ sensor) requires 3-5 Ca²⁺ ions to bind
|
||
- **SNARE complex** zippering is thermally driven and probabilistic
|
||
- These molecular processes have intrinsic randomness at nanoscale
|
||
|
||
### **3. Vesicle State Stochasticity**
|
||
|
||
- Vesicles exist in different "readiness states":
|
||
- **Docked & primed** (immediately releasable)
|
||
- **Docked but unprimed**
|
||
- **Reserve pool** (undocked)
|
||
- Transition between states is probabilistic
|
||
|
||
## **Why Evolution Selected Probabilistic Release**
|
||
|
||
### **Advantages of Low/Moderate Pr:**
|
||
|
||
1. **Dynamic Range:** Allows both **facilitation** (Pr increases with repeated spikes) and **depression** (Pr decreases with vesicle depletion)
|
||
2. **Noise Filtering:** Random failures filter out isolated, potentially noisy spikes while allowing bursts to get through (due to facilitation)
|
||
3. **Energy Efficiency:** Release machinery (vesicle fusion/recycling) is energetically expensive. Why waste energy on every spike?
|
||
4. **Information Capacity:** Probabilistic release allows synapses to encode information in **release probability** as well as spike rate
|
||
5. **Plasticity Substrate:** The stochastic nature provides a substrate for learning through Hebbian mechanisms
|
||
|
||
## **What Actually Gets Released When Release Occurs**
|
||
|
||
Even when release occurs, it's not always "all or nothing":
|
||
|
||
### **Quantal Release:**
|
||
|
||
- **Miniature EPSCs (mEPSCs):** Single vesicle release (~1000-5000 glutamate molecules)
|
||
- **Univesicular Release:** Most CNS synapses release **0 or 1 vesicle** per active zone per spike
|
||
- **Multivesicular Release:** Some synapses can release 2-3 vesicles simultaneously
|
||
|
||
### **Key Measurement:**
|
||
|
||
```
|
||
EPSC amplitude = Q × n × Pr
|
||
```
|
||
|
||
Where:
|
||
|
||
- **Q** = quantal size (response to one vesicle)
|
||
- **n** = number of release sites (active zones)
|
||
- **Pr** = release probability per site
|
||
|
||
## **How This Plays Out in Neural Computation**
|
||
|
||
### **Example: Cortical Pyramidal Neuron Synapse**
|
||
|
||
```
|
||
Spike train arrives: [1, 1, 1, 1, 1, 1] (6 spikes at 50 Hz)
|
||
|
||
With Pr = 0.3:
|
||
Actual releases might be: [0, 1, 0, 0, 1, 1]
|
||
|
||
Postsynaptic effect:
|
||
- Spike 1: No response
|
||
- Spike 2: EPSP
|
||
- Spike 3: No response
|
||
- Spike 4: No response
|
||
- Spike 5: EPSP
|
||
- Spike 6: EPSP
|
||
|
||
But due to facilitation:
|
||
Pr increases to 0.5 by spike 6
|
||
```
|
||
|
||
## **Simulation Implications**
|
||
|
||
In simulations, you would implement this as:
|
||
|
||
```python
|
||
import numpy as np
|
||
|
||
class Synapse:
|
||
def __init__(self, Pr=0.3):
|
||
self.Pr = Pr # Release probability
|
||
self.vesicles_available = True
|
||
|
||
def process_spike(self):
|
||
if not self.vesicles_available:
|
||
return 0 # No release due to depletion
|
||
|
||
# Probabilistic release decision
|
||
if np.random.random() < self.Pr:
|
||
# Release occurs
|
||
self.vesicles_available = False # Temporary depletion
|
||
self.trigger_recycle_timer() # Schedule vesicle recycling
|
||
return 1 # 1 vesicle released
|
||
else:
|
||
# Release fails probabilistically
|
||
return 0
|
||
```
|
||
|
||
## **Biological Determinants of Pr**
|
||
|
||
**High Pr synapses** tend to have:
|
||
|
||
- Denser VGCC clustering near release sites
|
||
- Higher Ca²⁺ sensitivity of Synaptotagmin
|
||
- More efficient priming machinery (Munc13)
|
||
- Larger readily releasable pool
|
||
|
||
**Low Pr synapses** tend to have:
|
||
|
||
- Sparse VGCC distribution
|
||
- Lower Ca²⁺ sensitivity
|
||
- Less efficient priming
|
||
- Smaller readily releasable pool
|
||
|
||
## **The Big Picture**
|
||
|
||
**Pr is the synapse's "transmission reliability setting"** that:
|
||
|
||
1. **Filters** spike trains probabilistically
|
||
2. **Encodes** short-term plasticity through dynamic changes
|
||
3. **Embeds** long-term memory through stable modifications
|
||
4. **Conserves** energy by not releasing on every spike
|
||
|
||
This stochasticity isn't a bug—it's a feature that allows synapses to be **temporal filters, memory elements, and computational units** all at once. The fact that transmission isn't guaranteed is precisely what gives synapses their rich computational properties, enabling phenomena like paired-pulse facilitation, synaptic filtering of high-frequency bursts, and providing a substrate for Hebbian learning through coincident detection failures. |