# **Detailed Temporal Dynamics of Postsynaptic Response and Plasticity**

*From glutamate binding to structural consolidation, with concentration changes, receptor trafficking, and calcium signaling across timescales*

---

## **Baseline State (Resting Spine)**

**Time:** Continuous  
**Postsynaptic [Ca²⁺]:** ~50-100 nM  
**Membrane Potential (Vₘ):** -70 mV  
**AMPARs in PSD:** 10-20 receptors (GluA1/GluA2 heteromers)  
**NMDARs in PSD:** 5-10 receptors (GluN1/GluN2B)  
**Mg²⁺ block of NMDARs:** ~80% at -70 mV  
**CaMKII state:** Mostly inactive (α:β ≈ 3:1 ratio)  
**PSD-95 clusters:** ~300 molecules per PSD

---

## **PHASE 1: FAST TIMESCALE (0-100 ms) - RECEPTOR ACTIVATION**

### **0.0-0.2 ms: Glutamate Arrival and Binding**

```
Presynaptic glutamate release (~5000 molecules)
    ↓
Diffusion across 20 nm synaptic cleft (t ≈ 0.1 ms)
    ↓
**Glutamate concentration in cleft:**
- Peak: 1-3 mM at PSD surface
- Rapid clearance by EAATs (t½ ≈ 1 ms)
    ↓
**Simultaneous binding to:**
1. **AMPARs (ionotropic, fast):**
   - 2 glutamate molecules bind per channel
   - Binding Kd ≈ 500 µM
   - Channel opens in ~0.2 ms
   
2. **NMDARs (ionotropic, slow):**
   - Requires glutamate + glycine/D-serine
   - Binding Kd ≈ 1-5 µM
   - Mg²⁺ block prevents opening at rest
   
3. **mGluRs (metabotropic):**
   - Group I mGluRs (mGluR1/5)
   - G-protein coupled, slower signaling
```

### **0.2-2.0 ms: AMPAR-Mediated Depolarization**

```
**For each open AMPAR:**
- Conductance: 8-12 pS (single channel)
- Reversal potential: 0 mV
- **Na⁺ influx:** ~3000 ions/channel/ms
- K⁺ efflux: ~1000 ions/channel/ms

**Net effect at spine head:**
Without other inputs: EPSP amplitude = 0.5-2 mV
With 20 AMPARs open: Current = 10-30 pA
Depolarization to Vₘ ≈ -60 mV
```

### **1.0-5.0 ms: NMDAR Activation (if depolarized)**

```
**Requirement:** Vₘ > -40 mV to relieve Mg²⁺ block
**Coincidence detection window:** 5-10 ms

If depolarized (from AMPARs or bAP):
    ↓
Mg²⁺ expelled from NMDAR channel
    ↓
**NMDAR opens with characteristic:**
- Slow kinetics (τrise ≈ 10 ms, τdecay ≈ 50-100 ms)
- High Ca²⁺ permeability (PCa/PNa ≈ 10:1)
- **Single channel Ca²⁺ influx:** ~5000 Ca²⁺ ions/ms
    ↓
**Local [Ca²⁺] in spine head:**
- Baseline: 100 nM
- With NMDAR activation: **→ 1-10 µM**
- With NMDAR + bAP coincidence: **→ 10-30 µM**
```

### **5.0-50 ms: Calcium Dynamics and Clearance**

```
**Calcium sources in spine:**
1. NMDARs (main source for plasticity)
2. Voltage-gated Ca²⁺ channels (VGCCs) from bAP
3. Internal stores (IP₃R, RyR)

**Calcium buffers in spine:**
- Calbindin-D28K (Kd ≈ 200 nM)
- Parvalbumin (Kd ≈ 10 nM)
- Calmodulin (Ca²⁺ sensor, Kd ≈ 1-10 µM)

**Clearance mechanisms:**
1. Plasma Membrane Ca²⁺ ATPase (PMCA): 
   - High affinity (Kd ≈ 100 nM)
   - Slow: clears ~30 Ca²⁺/sec per pump
   
2. Sodium-Calcium Exchanger (NCX):
   - Low affinity (Kd ≈ 1 µM) 
   - Fast: 3 Na⁺ in, 1 Ca²⁺ out
   
3. SERCA pumps into ER:
   - If spine has smooth ER
   
4. Mitochondrial uptake (larger spines):
   - MCU (mitochondrial Ca²⁺ uniporter)
   - Kd ≈ 10-20 µM

**Result:**
- 90% Ca²⁺ cleared in 50-100 ms
- Returns to baseline [Ca²⁺] in 200-500 ms
```

---

## **PHASE 2: MEDIUM TIMESCALE (100 ms - 10 sec) - SIGNALING CASCADES**

### **Calcium-Decoded Plasticity Decision**

```
**The "Calcium Rule":**
[Ca²⁺] amplitude × duration → plasticity direction

**Thresholds:**
- LTD: 1-5 µM sustained (100 ms - 1 sec)
- LTP: >10 µM brief (10-50 ms)
- LTP requires **rapid rise** (d[Ca²⁺]/dt > 0.5 µM/ms)
```

### **LTD Pathway (Moderate Ca²⁺)**

```
[Ca²⁺] = 1-5 µM for >100 ms
    ↓
Calcium binds Calmodulin (CaM)
    ↓
**Activates Calcineurin (CaN, PP2B):**
- Phosphatase, Kd ≈ 0.5 µM Ca²⁺
- Activated at lower [Ca²⁺] than CaMKII
    ↓
CaN dephosphorylates Inhibitor-1
    ↓
**Releases inhibition of Protein Phosphatase-1 (PP1)**
    ↓
PP1 dephosphorylates:
1. GluA1 at S845 → increases endocytosis
2. Stargazin → reduces AMPAR synaptic retention
3. Other targets promoting AMPAR removal
    ↓
**Result: AMPAR internalization begins in 30-60 sec**
```

### **LTP Pathway (High Ca²⁺)**

```
[Ca²⁺] > 10 µM with rapid rise
    ↓
Calcium binds Calmodulin (CaM)
    ↓
**Activates Ca²⁺/Calmodulin Kinase II (CaMKII):**
- 12-subunit holoenzyme
- Each subunit has autoinhibitory domain
- Requires Ca²⁺/CaM binding to activate
    ↓
**Autophosphorylation at T286:**
- First subunit phosphorylates neighbor
- Creates Ca²⁺-independent activity
- **Molecular switch:** stays active after Ca²⁺ clears
    ↓
**Active CaMKII translocates to PSD:**
- Binds to NR2B subunit of NMDAR
- Binds to α-actinin (actin linker)
- Becomes structural component of PSD
```

---

## **PHASE 3: SLOW TIMESCALE (10 sec - 10 min) - RECEPTOR TRAFFICKING**

### **LTD Execution (1-10 minutes)**

```
**Clathrin-mediated endocytosis:**
PP1 activity → GluA1 S845 dephosphorylated
    ↓
Increased binding to AP2 adaptor complex
    ↓
**Clathrin coats form at spine periphery (t ≈ 1-2 min)**
    ↓
AMPARs internalized via endocytosis
    ↓
**Vesicles transported to early endosomes**
    ↓
Receptors either:
1. Recycled back to surface (silent synapses)
2. Degraded in lysosomes (long-term LTD)
    ↓
**By 10 min:**
- 30-50% reduction in surface AMPARs
- EPSP amplitude decreases proportionally
```

### **LTP Execution (1-10 minutes)**

```
**Rapid AMPAR insertion:**
CaMKII phosphorylates:
1. **Stargazin (TARP γ-2) at S9:**
   - Increases binding to PSD-95
   - **Traps AMPARs in PSD** (Kd improves 10×)
   
2. **SynGAP (RasGAP):**
   - Phosphorylation inhibits Ras inactivation
   - Increases ERK/MAPK signaling
    ↓
**Exocytosis of AMPARs:**
1. From recycling endosomes (Rab11-dependent)
2. From intracellular pools
3. **Insertion at extrasynaptic sites first**
    ↓
**Lateral diffusion into PSD:**
- AMPARs diffuse in membrane (D ≈ 0.1 µm²/s)
- Phosphorylated Stargazin binds PSD-95
- **Trapped in PSD for minutes-hours**
    ↓
**By 10 min:**
- 50-100% increase in surface AMPARs
- EPSP amplitude increases 50-200%
```

### **Phosphorylation State Changes**

```
**AMPAR modifications during LTP:**
- **GluA1 S831:** Phosphorylated by CaMKII/PKC
  → Increases single channel conductance (γ from 8→12 pS)
  
- **GluA1 S845:** Phosphorylated by PKA
  → Increases open probability (Po from 0.8→0.95)
  
- **GluA2 S880:** Phosphorylated by PKC
  → Regulates binding to GRIP/ABP vs PICK1
```

---

## **PHASE 4: METABOLIC SUPPORT (10 min - 2 hours) - PROTEIN SYNTHESIS**

### **Local Translation in Spine**

```
**Trigger:** 
1. CaMKII activation
2. mGluR activation
3. BDNF-TrkB signaling

**Pathways:**
1. **mTOR pathway:** 
   - PI3K → Akt → mTORC1
   - Phosphorylates 4E-BP, releases eIF4E
   - **Initiates cap-dependent translation**
   
2. **MAPK pathway:**
   - Ras → Raf → MEK → ERK
   - Phosphorylates translation factors
    ↓
**Dendritic mRNA translation begins (t ≈ 20-30 min):**
Key mRNAs locally translated:
1. **CaMKIIα** - more kinase molecules
2. **GluA1** - new AMPAR subunits
3. **Arc/Arg3.1** - regulates AMPAR trafficking
4. **PSD-95** - scaffolding protein
5. **Homer1a** - regulates mGluR signaling
    ↓
**New proteins synthesized locally:**
- Concentration increases over 1-2 hours
- Replaces initial plasticity with stable changes
```

### **Retrograde Signaling Synthesis**

```
**For LTP:**
Ca²⁺ → activates nNOS (neuronal nitric oxide synthase)
    ↓
**NO synthesis from arginine:**
- Diffusion constant: ~3300 µm²/s
- Half-life: ~1-5 seconds
- Diffuses 10-20 µm to presynaptic terminal
    ↓
**BDNF synthesis and release:**
- Transcription begins in 30 min
- Release occurs 1-2 hours post-induction
```

---

## **PHASE 5: STRUCTURAL CONSOLIDATION (2 hours - 24 hours)**

### **Actin Cytoskeleton Remodeling**

```
**Spine enlargement (LTP):**
Active CaMKII → phosphorylates **Profilin**
    ↓
Profilin binds actin monomers → promotes polymerization
    ↓
**Rho GTPase activation:**
- Rac1 activated → promotes actin branching (via Arp2/3)
- Cdc42 activated → promotes filopodia formation
    ↓
**Actin polymerization in spine head:**
- F-actin increases 2-3×
- Spine volume increases over 1-3 hours
    ↓
**PSD expansion:**
- More space for AMPARs
- More PSD-95 scaffolding
    ↓
**By 6 hours:** Spine volume increased 50-100%
```

### **Nuclear Signaling and Gene Expression**

```
**Signals reach nucleus (1-3 hours):**
1. **CaMKIV translocation:** 
   - Activated by Ca²⁺ in dendrites
   - Translocates to nucleus when phosphorylated
   
2. **MAPK/ERK translocation:**
   - Activated at synapse
   - Travels to nucleus (active transport)
   
3. **CREB phosphorylation:**
   - At S133 by CaMKIV/PKA/RSK
   - Recruits CBP/p300 coactivators
    ↓
**Transcriptional activation (3-6 hours):**
Early genes (IEGs):
- c-Fos, c-Jun, Egr1/Zif268

Late genes (plasticity-related):
- **BDNF** (brain-derived neurotrophic factor)
- **GluA1** (AMPAR subunit)
- **CaMKIIα**
- **Arc**
- **Homer1a**
    ↓
**New proteins synthesized in soma (6-12 hours)**
    ↓
**Transport to dendrites (12-24 hours)**
    ↓
**Incorporation into spine (24+ hours)**
```

---

## **PHASE 6: VERY SLOW TIMESCALE (Days - Weeks) - STRUCTURAL STABILITY**

### **Spine Maturation and Stabilization**

```
**Day 1-7:**
- **PSD thickening:** from 30 nm → 50 nm
- **AMPAR subtype switch:** 
  GluA2-lacking (Ca²⁺-permeable) → GluA2-containing
  (Occurs over days via subunit replacement)
  
- **Synaptic adhesion molecules:**
  Neuroligin-Neurexin complexes stabilize contact
  
**Week 1-4:**
- **Spine shape changes:**
  Thin → Mushroom (LTP)
  Mushroom → Thin (LTD)
  
- **Presynaptic coordination:**
  Active zone aligns with expanded PSD
  
- **Perisynaptic astrocyte processes:**
  Enwrap mature synapse for metabolic support
```

### **Homeostatic Scaling**

```
**Days 2-7:**
If overall neuron firing rate changes significantly:
    ↓
**Global scaling mechanisms:**
1. **TNFα signaling:** from astrocytes
2. **BDNF level changes**
    ↓
All synapses on neuron scaled up or down
    ↓
**AMPAR number adjusted** while relative differences maintained
    ↓
**Preserves signal-to-noise ratio** of individual synapses
```

---

## **COMPLETE LTP TIMELINE EXAMPLE**

### **Induction (Seconds)**

```
T=0 ms: Presynaptic glutamate release
T=10 ms: bAP arrives at spine (coincidence)
T=15 ms: [Ca²⁺] peaks at 25 µM
T=50 ms: Ca²⁺ clears to 1 µM
T=1 sec: CaMKII autophosphorylated (T286)
T=10 sec: CaMKII translocates to PSD
```

### **Early Expression (Minutes)**

```
T=1 min: AMPARs inserted (from recycling endosomes)
T=2 min: EPSP amplitude increases 100%
T=5 min: Stargazin phosphorylated, AMPARs trapped
T=10 min: Early LTP established
```

### **Protein Synthesis-Dependent Phase (Hours)**

```
T=30 min: Local translation begins (CaMKIIα, GluA1)
T=1 hour: BDNF transcription initiated
T=2 hours: Spine volume begins increasing
T=3 hours: New proteins from local synthesis incorporated
T=6 hours: Spine volume increased 60%
```

### **Late Maintenance (Days)**

```
T=12 hours: New proteins from soma arrive
T=24 hours: Structural changes stabilized
T=48 hours: GluA2 subunits replace GluA1 homomers
T=7 days: Mature mushroom spine established
```

---

## **CALCIUM SIGNALING THRESHOLDS SUMMARY**

| \[Ca²⁺\] Range | Duration       | Sensor      | Outcome                    |
|----------------|----------------|-------------|----------------------------|
| < 0.5 µM       | Any            | None        | Baseline signaling         |
| 0.5-1 µM       | \>1 sec        | Calcineurin | Weak LTD                   |
| 1-5 µM         | 100 ms-1 sec   | Calcineurin | Strong LTD                 |
| 5-10 µM        | Brief (<50 ms) | CaMKII      | Weak LTP                   |
| \>10 µM        | Brief (<50 ms) | CaMKII      | Strong LTP                 |
| \>20 µM        | Any            | Calpain     | Pathological, spine damage |

---

## **KEY BIOLOGICAL PRINCIPLES**

1. **Spine as Biochemical Compartment:**
   - Neck resistance (50-500 MΩ) restricts diffusion
   - Allows independent [Ca²⁺] signaling in each spine
   - Enables synapse-specific plasticity
2. **Kinetic Competition:**
   - Calcineurin activates faster at low [Ca²⁺] (Kd ≈ 0.5 µM)
   - CaMKII requires higher [Ca²⁺] but has positive feedback
   - Winner-takes-all decision based on [Ca²⁺] time course
3. **Energy Requirements:**
   - Each AMPAR insertion: ~1000 ATP
   - CaMKII autophosphorylation: 1 ATP/subunit
   - Protein synthesis: ~4 ATP/amino acid
   - ATP supplied by astrocyte lactate
4. **Timescale Coupling:**
   - Fast (ms): Receptor activation
   - Medium (min): Trafficking existing proteins
   - Slow (hours): Making new proteins
   - Very slow (days): Structural changes

This postsynaptic timeline shows how a brief glutamate signal triggers a cascade of events across multiple timescales, converting transient electrical activity into lasting structural and functional changes that underlie learning and memory.