# **Spike Train Examples: How Different Patterns Lead to LTP, LTD, or Tagging**

Here's a clear visualization of how **specific spike train patterns** produce the different calcium dynamics and plasticity outcomes:

```mermaid
timeline
    title Spike Train Patterns & Plasticity Outcomes
    section LTP Induction (Pre-before-Post Burst)
        Pre-spikes : 100 Hz burst<br>0, 10, 20, 30, 40 ms
        Post-spike : Single bAP at 15 ms
        Ca²⁺ Dynamics : Rapid rise to 5-10 μM<br>within 20 ms
        Tag Window : Tag set at 5 ms<br>Active until 105 ms
        Outcome : Strong LTP<br>200-300% AMPAR increase
    section LTD Induction (Isolated Presynaptic Train)
        Pre-spikes : 10 Hz train for 1s<br>0, 100, 200...900 ms
        Post-spikes : None
        Ca²⁺ Dynamics : Sustained 1-2 μM<br>for ~500 ms
        Tag Window : Multiple tags set<br>but no coincidence
        Outcome : Moderate LTD<br>40-60% AMPAR removal
    section Tagging Only (Poorly Timed Activity)
        Pre-spikes : 50 Hz burst<br>0, 20, 40 ms
        Post-spike : Delayed at 100 ms
        Ca²⁺ Dynamics : Brief 0.8-1 μM peak
        Tag Window : Tag set at 20 ms<br>Expires before post-spike
        Outcome : Metaplastic priming only<br>No weight change
```

---

## **EXAMPLE 1: LTP INDUCTION (Theta Burst Pattern)**

**Spike trains:**

```
Presynaptic:   ●    ●    ●    ●    ●    (100 Hz burst: 0, 10, 20, 30, 40 ms)
Postsynaptic:        ↑bAP at 15 ms
```

**Calcium timeline:**

```
Time (ms)   Ca²⁺ (μM)   Event
────────────────────────────────────
0           0.1 → 1.0   Spike 1: Glutamate → NMDAR opens
10          1.0 → 3.0   Spike 2: Summation + tag set (θ_tag crossed)
15          3.0 → 8.0   bAP arrives → Mg²⁺ block fully relieved
20          8.0 → 12.0  Spike 3: Maximum Ca²⁺ → crosses θ_LTP
30          12.0        Spike 4: High plateau
40          10.0        Spike 5: High sustained
50          5.0         Decay begins
100         0.5         Tag window closes
```

**Why LTP occurs:**

- **Strong coincidence**: bAP arrives during glutamate presence (Δt = +5 ms)
- **High Ca²⁺ peak**: 8-12 μM > θ\_LTP (2 μM)
- **Tag active**: Set at ~10 ms, active until ~110 ms
- **Protein synthesis**: Triggered by combined Ca²⁺ + neuromodulators

**Outcome:** 200-300% increase in AMPARs within 5-30 minutes.

---

## **EXAMPLE 2: LTD INDUCTION (Low-Frequency Train)**

**Spike trains:**

```
Presynaptic:   ●     ●     ●     ●     ●     ●     ●     ●     ●     ●
               0    100   200   300   400   500   600   700   800   900 ms
Postsynaptic:   (None - isolated presynaptic activity)
```

**Calcium timeline:**

```
Time (ms)   Ca²⁺ (μM)   Event
────────────────────────────────────
0           0.1 → 1.5   Spike 1: Tag set at ~5 ms
100         1.5 → 2.0   Spike 2: Sustained moderate Ca²⁺
200         2.0         Spike 3: LTD threshold duration starts
300         2.0         Spike 4: Sustained >100 ms → LTD engaged
400         2.0         Spike 5: Calcineurin fully active
500         1.8         Spike 6: AMPAR removal begins
...
900         1.5         Last spike
1000        0.8         Decay begins
1500        0.2         Back to baseline
```

**Why LTD occurs:**

- **No coincidence**: No bAPs to relieve Mg²⁺ block fully
- **Moderate, sustained Ca²⁺**: 1.5-2.0 μM for >500 ms
- **Calcineurin activation**: Requires sustained moderate Ca²⁺
- **No LTP trigger**: Ca²⁺ never exceeds θ\_LTP (2 μM)

**Outcome:** 40-60% AMPAR removal within 1-5 minutes.

---

## **EXAMPLE 3: TAG WITHOUT EXPRESSION (Mistimed Activity)**

**Spike trains:**

```
Presynaptic:   ●     ●     ●
               0     20    40 ms
Postsynaptic:                        ↑bAP at 100 ms (too late)
```

**Calcium timeline:**

```
Time (ms)   Ca²⁺ (μM)   Event
────────────────────────────────────
0           0.1 → 0.6   Spike 1: Below tag threshold
20          0.6 → 1.0   Spike 2: Tag SET (θ_tag = 0.5 μM)
40          1.0 → 1.2   Spike 3: Tag active, Ca²⁺ moderate
50          0.8         Decay begins
100         0.3         bAP arrives alone → small Ca²⁺ via VGCCs
105         0.4         Insufficient for LTP
110         0.3         Tag EXPIRES (set at 20 ms, 90 ms lifetime)
```

**Why only tagging occurs:**

- **Tag set**: Moderate Ca²⁺ (1.0 μM) sets eligibility
- **No coincidence**: bAP arrives 60 ms after last glutamate
- **Ca²⁺ insufficient**: bAP alone → ~0.4 μM (well below θ\_LTP)
- **Tag expires**: No strong Ca²⁺ within ~100 ms window

**Outcome:** No weight change, but spine is **primed**:

- Lowered θ\_LTP for next 30-60 minutes
- Increased kinase sensitivity
- **Next coincident event** will produce enhanced LTP

---

## **EXAMPLE 4: STDP WINDOW DEMONSTRATION**

**Different Δt values produce different outcomes:**

### **A. Δt = +10 ms (Pre-before-Post): LTP**

```
Pre:  ●
        ↘
Post:    ● (10 ms later)
Ca²⁺:  0 → 8 μM → LTP
```

### **B. Δt = +50 ms (Pre-before-Post): Weak Tag Only**

```
Pre:  ●
            ↘
Post:        ● (50 ms later)
Ca²⁺:  0 → 1 μM → tag → 0.5 μM from bAP → No LTP (too low)
```

### **C. Δt = -10 ms (Post-before-Pre): LTD**

```
Post:  ●
         ↘
Pre:      ● (10 ms later)
Ca²⁺:  0 → 1.5 μM (VGCC) → + 1.0 μM (NMDAR) → Sustained 2.5 μM → LTD
```

### **D. Δt = -50 ms (Post-before-Pre): Nothing**

```
Post:  ●
                 ↘
Pre:               ● (50 ms later)
Ca²⁺:  Separate transients (0.5 μM each) → No tag, no LTD
```

---

## **EXAMPLE 5: SPIKE FREQUENCY EFFECTS**

### **Low frequency (1 Hz): Steady state**

```
Pre:  ●    ●    ●    ●    ●    ●    ●
Time: |----|----|----|----|----|----|
Ca²⁺: Each transient ~0.8 μM, decays fully between spikes
Outcome: No plasticity (below θ_tag most of the time)
```

### **Moderate frequency (10 Hz): LTD**

```
Pre:  ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
      (sustained for 1 second)
Ca²⁺: Builds to 1.5-2.0 μM plateau, sustained >500 ms
Outcome: Moderate LTD
```

### **High frequency burst (100 Hz): LTP**

```
Pre:  [●●●●●]        [●●●●●]        [●●●●●]
      Burst 1        Burst 2        Burst 3
Post: ↑bAP during each burst
Ca²⁺: Peaks at 10+ μM during bursts, decays partially between
Outcome: Strong LTP
```

### **Irregular Poisson-like: Mixed**

```
Pre:  ●   ● ●    ●     ● ●   ●    ●  ●
      (average 20 Hz, irregular intervals)
Ca²⁺: Variable, depends on recent history
Outcome: Some facilitation/depression, minimal long-term change
```

---

## **EXAMPLE 6: NEUROMODULATOR EFFECTS ON SPIKE TRAINS**

### **With Dopamine (enhances LTP):**

```
Pre:  ●    ●    ●    ●    ●    (20 Hz train)
Post:        ↑bAP at 15 ms
DA:   └──────────→ High during train
Effect: Ca²⁺ peaks 30% higher, tag lifetime extended
Outcome: LTP where none would occur without DA
```

### **With eCB (promotes LTD):**

```
Pre:  ●    ●    ●    ●    ●    ●    (30 Hz train)
Post:        ↑bAP at 10 ms → eCB synthesis
eCB:                 └────→ (50 ms delay) inhibits presynaptic Ca²⁺
Effect: Later spikes see reduced Ca²⁺ influx
Outcome: Weaker LTP or mixed LTP/LTD
```

---

## **SUMMARY TABLE: SPIKE TRAIN → OUTCOME MAPPING**

| Pattern         | Frequency   | Coincidence    | Ca²⁺ Dynamics                | Tag           | Outcome                    |
|-----------------|-------------|----------------|------------------------------|---------------|----------------------------|
| **Single pair**     | N/A         | Δt = +10 ms    | Brief 5-10 μM spike          | Set + used    | LTP                        |
| **Single pair**     | N/A         | Δt = -10 ms    | Sustained 1-2 μM             | Set           | LTD                        |
| **Theta burst**     | 5 Hz bursts | bAP in burst   | High bursts, moderate gaps   | Multiple tags | Strong LTP                 |
| **Low frequency**   | 1 Hz        | None           | Separate 0.5-1 μM transients | None          | No change                  |
| **Sustained 10 Hz** | 10 Hz       | None           | Plateau ~1.5-2.0 μM          | Multiple tags | LTD                        |
| **High frequency**  | 100 Hz      | None           | Initial high then depression | Early tags    | Mixed: LTP then depression |
| **Mistimed burst**  | 50 Hz       | bAP 60 ms late | Moderate then low            | Expired       | Metaplasticity only        |

---

## **KEY PRINCIPLES FROM THESE EXAMPLES:**

1. **Timing precision matters:** ±20 ms windows determine LTP vs LTD
2. **Frequency matters:** Low frequencies favor LTD, bursts favor LTP
3. **History matters:** Recent spikes determine current Ca²⁺ baseline
4. **Tag lifetime is critical:** ~100 ms window for coincidence detection
5. **Nonlinear summation:** Bursts ≠ sum of individual spikes

**The presynapse-postsynapse system acts as a sophisticated pattern detector:**

- **Detects coincidences** within 100 ms → LTP
- **Detects isolated presynaptic activity** → LTD
- **Detects moderate activity without coincidence** → Metaplastic priming
- **All filtered through neuromodulatory state** (DA, eCB, etc.)

**This explains why specific spike patterns in the brain (theta rhythms, gamma bursts) are so effective for learning—they naturally create the calcium dynamics that trigger LTP with minimal depression.**