# VARIABLES

## **MILLISECOND SCALE (Action Potential → Release)**

| Variable          | Direct Behavior/Effect                                                       | Modulated By (Same Scale)                                   | Modulated By (Other Scales)                                                                         |
|-------------------|------------------------------------------------------------------------------|-------------------------------------------------------------|-----------------------------------------------------------------------------------------------------|
| **V_mem**             | • AP depolarization<br />• K⁺-mediated repolarization                        | • **KChannels** activation<br />• Na⁺ channel inactivation      | • **ATP** (seconds) - powers Na⁺/K⁺ pump<br />• **K+** accumulation (tens-ms)                               |
| **VGCC**              | • Ca²⁺ influx triggered by depolarization<br />• Ca²⁺-dependent inactivation | • **V_mem** (depolarization)<br />• **Ca+** microdomain (feedback)  | • **VGCC invagination** (hours) - reduces surface expression<br />• **BDNF** (hours) - increases expression |
| **Ca+** (microdomain) | • Rapid spike near VGCCs (~10-100 μM)<br />• Triggers vesicle fusion         | • **VGCC** opening kinetics<br />• Endogenous buffers           | • **CaChannels** density (hours)<br />• **NO** (seconds) - modulates channel opening                        |
| **Vesicles** (fusion) | • SNARE-mediated fusion with membrane<br />• Release probability (Pr) varies | • **Ca+** concentration⁴<br />• **RRP** position/docking            | • **ATP** (seconds) - fuels priming<br />• **eCB** (seconds) - inhibits release                             |
| **K+** (efflux)       | • Repolarization via KChannels<br />• Clears AP                              | • **V_mem** (depolarization)<br />• **Ca+** (activates SK channels) | • **KChannels** modulation (minutes)                                                                    |
| **KChannels**         | • Voltage-gated opening<br />• Ca²⁺-activated (SK)                           | • **V_mem**<br />• **Ca+** microdomain                              | • **Phosphorylation** (minutes)<br />• **BDNF** (hours) - modulates expression                              |

## **TENS-HUNDREDS OF MILLISECONDS SCALE (Short-term Dynamics)**

| Variable                | Direct Behavior/Effect                                                               | Modulated By (Same Scale)                                     | Modulated By (Other Scales)                                                                          |
|-------------------------|--------------------------------------------------------------------------------------|---------------------------------------------------------------|------------------------------------------------------------------------------------------------------|
| **Ca+** (global)            | • Bulk terminal increase (~0.5-2 μM)<br />• Activates mobilization                   | • Diffusion from microdomains<br />• PMCA/NCX pumps           | • **ATP** (seconds) - fuels pumps<br />• **Lactate** (seconds) - supports mitochondrial uptake               |
| **Vesicles** (mobilization) | • Movement from **RP** → **RRP**<br />• Docked vesicles become release-ready                 | • **Ca+** global concentration<br />• **RRP** depletion state         | • **Mobilization rate** (hours) - structural adaptation<br />• **ATP** (seconds) - fuels transport           |
| **RRP**                     | • Immediate release pool (~5-15 vesicles)<br />• Depletes with high-frequency firing | • **Vesicles** release (ms)<br />• **Vesicles** mobilization into RRP | • **RP** size (minutes)<br />• **BDNF** (hours) - increases docking sites                                    |
| **K+** (cleft accumulation) | • Extracellular K⁺ rises to ~8-12 mM<br />• Affects resting potential                | • **KChannels** activity (ms)<br />• Astrocyte/glia uptake        | • **Activity history** (minutes) - astrocyte adaptation                                                  |
| **eCB**                     | • Retrograde diffusion to presynapse<br />• Binds CB1 receptors (~100-500 ms)        | • Postsynaptic Ca²⁺ rise (ms)<br />• mGluR activation         | • **Activity patterns** (minutes) - regulates production<br />• **NO** (seconds) - can enhance eCB synthesis |

## **SECONDS-MINUTES SCALE (Metabolic & Signaling)**

| Variable         | Direct Behavior/Effect                                                                      | Modulated By (Same Scale)                                              | Modulated By (Other Scales)                                                               |
|------------------|---------------------------------------------------------------------------------------------|------------------------------------------------------------------------|-------------------------------------------------------------------------------------------|
| **ATP**              | • Fuels: pumps, vesicle cycling, protein phosphorylation<br />• Depletes with high activity | • **Lactate** conversion<br />• Mitochondrial respiration                  | • **Activity demand** (ms scale)<br />• **BDNF** (hours) - enhances mitochondrial function        |
| **Lactate**          | • Astrocyte→neuron shuttle<br />• Converted to pyruvate for ATP                             | • Glutamate uptake by astrocytes<br />• Glycogen breakdown             | • **Activity level** (ms-min)<br />• **NO** (seconds) - regulates blood flow                      |
| **NO**               | • Retrograde diffusion from postsynapse<br />• Activates presynaptic cGMP pathways          | • Postsynaptic NOS activation by Ca²⁺<br />• NMDA receptor activity    | • **Activity patterns** (minutes)<br />• **BDNF** (hours) - regulates NOS expression              |
| **RP**               | • Reserve vesicle pool (~100-500 vesicles)<br />• Slowly replenishes RRP                    | • **Vesicles** recycling<br />• **Vesicles** mobilization out of RP            | • **RP capacity** (hours) - structural changes<br />• **ATP** (seconds) - fuels vesicle refilling |
| **BDNF**             | • Retrograde transport (slow)<br />• Activates TrkB receptors                               | • Activity-dependent release from postsynapse<br />• Local translation | • **Ca+** integration (minutes)<br />• **eCB** (minutes) - can modulate release                   |
| **eCB** (persistent) | • Long-term depression (LTD) induction<br />• Alters release probability                    | • Sustained postsynaptic activity<br />• DAG lipase activation         | • **NO** (seconds) - synergistic effects<br />• **BDNF** (hours) - can counteract eCB-LTD         |

## **SECONDS-HOURS-DAYS SCALE (Structural Modulation)**

| Variable                     | Modulatory Behavior                                              | Influenced By                                                                                            | Effects on Faster Scales                                                          |
|------------------------------|------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------|
| **VGCC** (invagination)          | • Internalization of channels<br />• Reduces release probability | • **Ca+** integral (minutes of activity)<br />• **BDNF** (trophic support)<br />• **eCB** (chronic signaling)        | • ↓ **Ca+** influx (ms)<br />• ↓ **Vesicles** release probability (ms)                    |
| **CaChannels** (density)         | • Changes in VGCC number at active zone                          | • **BDNF**-TrkB signaling (hours)<br />• Homeostatic scaling (days)<br />• Activity history (integrated **Ca+**) | • Alters **Ca+** microdomain (ms)<br />• Changes short-term plasticity (tens-ms)      |
| **RP** (pool size)               | • Structural changes in vesicle reserves                         | • **BDNF** (enhances)<br />• Chronic **eCB** (reduces)<br />• Metabolic capacity (**ATP/Lactate** supply)            | • Changes **RRP** refilling rate (tens-ms)<br />• Alters sustained release (seconds)  |
| **Vesicles** (mobilization rate) | • Faster/slower RP→RRP trafficking                               | • **BDNF**-cytoskeletal remodeling<br />• Synapsin phosphorylation state (**Ca+** history)                       | • Alters short-term facilitation/depression (tens-ms)                             |
| **KChannels** (expression)       | • Changes in Kv channel density                                  | • Activity-dependent gene regulation<br />• **BDNF** modulation<br />• **K+** homeostasis needs                  | • Alters AP waveform and duration (ms)<br />• Changes firing frequency adaptation |

## **CROSS-VARIABLE FEEDBACK LOOPS**

### **Fast Release → Metabolic Support Loop**

```
V_mem (AP) → VGCC opening → Ca+ influx → Vesicles release
  ↓
Glutamate release → Astrocyte activation → Lactate production
  ↓
Lactate → ATP synthesis → Fuels: VGCC recycling, Vesicles priming, Ca+ pumps
```

### **Activity → Structural Adaptation Loop**

```
High activity → Ca+ accumulation → BDNF release (post→pre)
  ↓
BDNF → ↑ VGCC expression, ↑ RP size, ↑ mobilization rate
  ↓
Enhanced release capacity → Changes Ca+ dynamics → Homeostatic adjustment
```

### **Retrograde Modulation Network**

```
Postsynaptic: Ca+ → NO production → Presynaptic: cGMP → Modulates VGCC
          ↓                                    ↓
Postsynaptic: Ca+ → eCB production → Presynaptic: CB1 → Inhibits VGCC, ↓ release
          ↓
Postsynaptic: Ca+ → BDNF synthesis → Presynaptic: TrkB → ↑ VGCC, ↑ RP
```

### **Energy-Redistribution Loop**

```
High activity → ATP depletion → Activates AMPK → ↑ Lactate uptake
      ↓                               ↓
Reduced release probability   ↑ Mitochondrial biogenesis (days)
      ↓                               ↓
Lower Ca+ demand             Enhanced ATP production
```

## **KEY VARIABLE INTERDEPENDENCIES**

1. **VGCC** ↔ **Ca+** (bidirectional):
   - VGCC opening → Ca+ influx
   - Ca+ accumulation → VGCC modulation (inactivation/adaptation)
2. **ATP** as universal modulator:
   - Required for: V_mem maintenance, Ca+ clearance, Vesicles cycling, RP refilling
   - Limited ATP → affects all faster processes
3. **BDNF** as structural organizer:
   - Coordinates: VGCC expression, RP size, KChannels density, metabolic capacity
4. **Ca+** as integration signal:
   - Fast: triggers Vesicles release (ms)
   - Medium: regulates Vesicles mobilization (tens-ms)
   - Slow: drives structural changes via BDNF/NO (minutes-hours)
5. **K+**/**KChannels** as activity brakes:
   - Regulate AP duration and frequency
   - Homeostatically adjusted based on activity history

This framework shows how your specified variables interact across timescales, with each variable playing multiple roles depending on the temporal context.

---

---

---

# **ATP: The Multiscale Energy Integrator**

## **ATP's Roles Across Temporal Scales**

### **1. MILLISECOND SCALE (Emergency Power)**

**Direct Behaviors Enabled:**

- **VGCC recovery**: Rapid phosphorylation/dephosphorylation cycles
- **SNARE priming**: ATP hydrolysis by NSF for vesicle fusion competence
- **Na⁺/K⁺ pump**: Immediate AP recovery (3 Na⁺ out, 2 K⁺ in per ATP)

**Influences on Other Variables:**

- ↓ **ATP** → Slower **V_mem** repolarization (K⁺ pump impaired)
- ↓ **ATP** → Reduced **VGCC** recovery from inactivation
- ↓ **ATP** → Impaired **Vesicles** priming → ↓ release probability

**Critical Threshold:** <0.1s depletion → immediate release failure

### **2. TENS-HUNDREDS OF MS SCALE (Short-term Energy Buffer)**

**Direct Behaviors Enabled:**

- **Ca²⁺ clearance**: PMCA pumps (1 Ca²⁺ out per ATP)
- **Vesicle mobilization**: Myosin/kinesin ATPases for RP→RRP movement
- **Endocytosis initiation**: Clathrin coat assembly (early phase)

**Energy Dynamics:**

- **Activity spike**: 1 AP → ~20,000 ATP molecules consumed
- **Buffer capacity**: ~10⁸ ATP molecules in terminal → supports ~500 APs
- **Recovery rate**: ~5 ATP/ms production at maximum mitochondrial output

**Cross-scale Coupling:**

- High **Ca+** influx → ↑ mitochondrial Ca²⁺ uptake → ↑ ATP production (seconds)
- **K+** accumulation → activates Na⁺/K⁺ pump → ↑ ATP demand
- **Lactate** conversion → ~15 ATP per lactate (delayed supply)

### **3. SECOND-MINUTE SCALE (Metabolic Regulation Hub)**

**Direct Behaviors Enabled:**

- **Vesicle recycling**: Complete endocytosis-exocytosis cycle (~30 ATP/vesicle)
- **Neurotransmitter reloading**: Vacuolar H⁺-ATPase (2 H⁺/ATP) → glutamate uptake
- **RP refilling**: New vesicle synthesis and transport

**Regulatory Functions:**

- **ATP/ADP ratio** as metabolic sensor: 
  - High ATP: AMPK inactive → growth/maintenance
  - Low ATP: AMPK active → emergency response, ↓ protein synthesis
- **Glycogen shunt**: Terminal glycogen → lactate (backup, seconds)
- **Mitochondrial positioning**: ATP gradients guide movement to active zones

**Modulation by Other Variables:**

- **BDNF** → ↑ mitochondrial biogenesis → ↑ ATP capacity (hours)
- **NO** → regulates cytochrome c oxidase → modulates ATP production
- **eCB** → CB1 receptors inhibit adenylate cyclase → ↓ ATP synthesis

### **4. HOURS-DAYS SCALE (Structural Energy Budget)**

**Direct Behaviors Enabled:**

- **Protein synthesis**: ~4 ATP per peptide bond → VGCCs, vesicle proteins
- **Organelle biogenesis**: Mitochondria, ER, vesicle pools
- **Axonal transport**: Kinesin/dynein motors (1 ATP/8 nm step)

**Long-term ATP Allocation Decisions:**

```
High activity + Adequate ATP → Investment in:
  1. More VGCCs (increased Ca²⁺ capacity)
  2. Larger RP (more vesicles)
  3. Additional mitochondria (future capacity)

High activity + Limited ATP → Conservation mode:
  1. VGCC invagination (lower Pr, save energy)
  2. Reduced RP size (lower maintenance cost)
  3. Enhanced lactate uptake (external energy)
```

**BDNF-ATP Synergy:**

- **BDNF** signals "importance" → allocates ATP to structural growth
- **ATP** availability determines BDNF effect magnitude
- **Negative feedback**: Low ATP → ↓ TrkB trafficking → ↓ BDNF sensitivity

## **ATP as Cross-Scale Communication Channel**

### **Energy Status Signaling:**

```
Fast signal (ms): ATP/ADP ratio at active zone → immediate release probability
Medium signal (s): AMPK activation → mobilize energy reserves
Slow signal (hours): PGC-1α activation → mitochondrial biogenesis
```

### **Activity-Energy Feedback Loops:**

**Positive Feedback (Dangerous):**

```
High activity → Ca²⁺ overload → mitochondrial damage → ↓ ATP
↓ ATP → impaired Ca²⁺ clearance → more Ca²⁺ overload → more damage
↓ ATP → reduced Na⁺/K⁺ pump → depolarization → more VGCC opening
Result: Excitotoxicity
```

**Negative Feedback (Protective):**

```
High activity → ATP depletion → AMPK activation
AMPK → ↓ protein synthesis (conserves ATP)
AMPK → ↑ glucose transporters (enhances supply)
AMPK → ↓ VGCC expression (reduces demand)
Result: Homeostasis
```

### **ATP-Dependent Plasticity Gates:**

**"Energy Checkpoint" for Structural Changes:**

```
Question: Should synapse grow?
Inputs: BDNF signal (importance) + Ca²⁺ history (activity) + ATP availability
Decision rule:
  IF (BDNF high AND ATP adequate) → GROW
  IF (BDNF high AND ATP low) → INVAGINATE (save energy)
  IF (BDNF low AND ATP high) → MAINTAIN
  IF (BDNF low AND ATP low) → SHRINK
```

## **Specific ATP ↔ Variable Interactions**

### **ATP ↔ Lactate (Critical Partnership)**

- **Astrocyte lactate** → neuron → pyruvate → 15 ATP via TCA cycle
- **Activity-dependent coupling**: Glutamate uptake → astrocyte glycolysis → lactate export
- **Timescale**: Seconds for lactate transport, minutes for glycogen mobilization

### **ATP ↔ VGCC (Bidirectional)**

- **ATP → VGCC**: Phosphorylation modulates opening kinetics (ms)
- **VGCC → ATP demand**: Each Ca²⁺ ion requires 1 ATP for extrusion
- **Homeostatic setpoint**: VGCC density adjusted to match ATP production capacity

### **ATP ↔ RP Size (Energy Budget)**

- **Storage cost**: ~100 ATP/day per vesicle (maintenance + turnover)
- **Allocation decision**: ATP surplus → more vesicles; deficit → fewer vesicles
- **Dynamic adjustment**: RP shrinks within hours of ATP shortage

### **ATP ↔ K⁺/KChannels (Stability Control)**

- **Na⁺/K⁺ pump**: 1 ATP clears 3 Na⁺, brings 2 K⁺
- **K⁺ accumulation** without ATP → depolarization → runaway excitation
- **KChannels** require ATP for phosphorylation-dependent modulation

## **Clinical/Experimental Implications**

**Energy-Limited Plasticity:**

- Learning under low ATP (sleep deprivation, metabolic stress) → less structural change
- High ATP + BDNF → optimal plasticity window

**Therapeutic Targets:**

- Enhance lactate shuttle → support ATP during high demand
- Modulate AMPK → shift energy allocation decisions
- Mitochondrial support → increase ATP capacity for structural changes

**Measurement Approaches:**

- **FRET ATP sensors**: Real-time ATP dynamics (seconds)
- **ATP/ADP ratio**: Metabolic status (minutes)
- **Mitochondrial density**: ATP capacity (hours-days)

## **Summary: ATP as Presynaptic "Bank Account"**

```
Quick cash (ms): ATP at active zone → immediate transactions
Checking account (100ms): Cytosolic ATP → short-term operations
Savings account (seconds): Mitochondrial/phosphocreatine → buffer
Investment portfolio (hours): Structural changes → long-term capacity
Credit line (emergency): Lactate shuttle → external support
```

The presynaptic terminal's ATP management strategy determines:

- **Release fidelity** (ms scale)
- **Short-term plasticity** (100ms scale)
- **Sustained transmission** (second scale)
- **Structural adaptation** (hour-day scale)

Every plasticity decision is fundamentally an energy allocation decision, with ATP serving as both the currency and the accountant.

---

---

---

# **Ca²⁺: The Universal Presynaptic Signal**

## **Ca²⁺ Across Temporal Scales**

### **1. MILLISECOND SCALE (Nano/Submicrodomain Ca²⁺)**

**Direct Behaviors Triggered:**

- **Vesicle fusion**: Cooperative binding to synaptotagmin (n~4)
- **KChannel activation**: SK channels open → fast afterhyperpolarization
- **VGCC feedback**: Ca²⁺-dependent inactivation (CDI)

**Dynamics:**

- **Rise time**: <100 μs to peak
- **Decay time constant**: 200-500 μs (fast buffers)
- **Diffusion coefficient**: ~200 μm²/s (buffered)

**Influences on Other Variables:**

```
Ca²⁺ (ms) → Vesicles release: Exponential dependence (EC₅₀ ~ 10-25 μM)
Ca²⁺ (ms) → KChannels (SK): Fast AHP → modulates next AP
Ca²⁺ (ms) → VGCC: CDI reduces subsequent Ca²⁺ influx
```

### **2. TENS-HUNDREDS OF MS SCALE (Global Terminal Ca²⁺)**

**Spatial Integration:**

- **Bulk concentration**: 0.2-2 μM throughout terminal
- **Residual Ca²⁺**: 0.1-0.5 μM between APs

**Direct Behaviors Enabled:**

- **Vesicle mobilization**: Ca²⁺-dependent phosphatase activation (calcineurin)
- **Short-term plasticity**: 
  - **Facilitation**: Residual Ca²⁺ binds to synaptotagmin priming
  - **Augmentation**: Sustained Ca²⁺ activates CaMKII
- **Metabolic coupling**: Mitochondrial Ca²⁺ uptake initiation

**Cross-scale Interactions:**

```
Ca²⁺ (100ms) → NO production: Activates postsynaptic NOS → retrograde signal
Ca²⁺ (100ms) → eCB synthesis: Postsynaptic DAG lipase activation
Ca²⁺ (100ms) → RP→RRP: Calcineurin dephosphorylates synapsin
Ca²⁺ (100ms) → ATP demand: Each Ca²⁺ extruded requires 1 ATP
```

**Mathematical Representation:**

```
d[Ca²⁺]_global/dt = J_influx - J_pump - J_mitochondria - J_diffusion
where:
  J_influx ∝ Σ(VGCC_open) over recent APs
  J_pump = V_max·[Ca²⁺]/(K_m + [Ca²⁺]) (ATP-dependent)
  J_mitochondria = k_m·[Ca²⁺]·(ΔΨ_m - threshold)
```

### **3. SECOND-MINUTE SCALE (Signaling Ca²⁺)**

**Direct Behaviors Enabled:**

- **Gene expression**: Nuclear Ca²⁺ → CREB phosphorylation
- **Metabolic regulation**: Mitochondrial matrix Ca²⁺ → TCA cycle enzymes
- **Structural tagging**: Local Ca²⁺ waves mark active synapses

**Signal Integration Mechanisms:**

- **Frequency decoding**: Ca²⁺ spikes → NFAT activation
- **Amplitude decoding**: High Ca²⁺ → CamKII autophosphorylation
- **Duration decoding**: Sustained Ca²⁺ → MAPK pathway activation

**Modulation by Other Variables:**

```
ATP ↓ → Reduced Ca²⁺ clearance → Elevated baseline Ca²⁺
BDNF → Enhances Ca²⁺ signals via PLCγ→IP₃→ER release
NO → cGMP → PKG → modulates Ca²⁺ channels and pumps
Lactate → Supports mitochondrial Ca²⁺ uptake via ATP
```

### **4. HOURS-DAYS SCALE (Ca²⁺ as Structural Organizer)**

**Direct Behaviors Enabled:**

- **Synapse growth/shrinkage**: Ca²⁺-dependent gene expression programs
- **Homeostatic scaling**: Chronic Ca²⁺ levels set VGCC density
- **Metaplasticity**: Ca²⁺ history determines future plasticity rules

**Ca²⁺ Setpoints and Homeostasis:**

- **Target baseline**: 50-100 nM (resting)
- **Activity setpoint**: Integrated over hours determines structural changes
- **Memory window**: Ca²⁺ history of last 24-48 hours influences current state

## **Ca²⁺ as Information Encoder**

### **Temporal Coding by Ca²⁺:**

**Amplitude Encoding:**

- Single AP: ~0.5 μM global Ca²⁺
- 10 Hz train: ~1.5 μM global Ca²⁺
- 100 Hz burst: >5 μM global Ca²⁺

**Frequency Encoding:**

- Low frequency (<1 Hz): Discrete Ca²⁺ transients
- Theta (4-8 Hz): Partial summation
- Gamma (30-100 Hz): Sustained elevation

**Duration Encoding:**

- Brief (<100 ms): Fast signaling only
- Medium (1-10 s): Activates kinases
- Long (>1 min): Triggers gene expression

### **Spatial Coding by Ca²⁺:**

**Microdomain vs Global Signals:**

```
VGCC cluster 1 → Ca²⁺ microdomain 1 → Vesicles 1-3
VGCC cluster 2 → Ca²⁺ microdomain 2 → Vesicles 4-6
Diffusion → Global Ca²⁺ → Mobilization, metabolic signals
```

**Compartmentalization:**

- **Active zone**: Release-triggering (fast)
- **Vesicle pools**: Mobilization (medium)
- **Mitochondria**: Metabolic coupling (slow)
- **Nucleus**: Gene regulation (very slow)

## **Ca²⁺ ↔ Specific Variable Interactions**

### **Ca²⁺ ↔ VGCC (Bidirectional Control)**

```
Fast (ms): Ca²⁺-dependent inactivation (CDI) - negative feedback
Medium (s): Ca²⁺-dependent facilitation (CDF) - positive feedback
Slow (hours): Ca²⁺-dependent VGCC expression - homeostatic
```

### **Ca²⁺ ↔ ATP (Energy-Coupling)**

- **Ca²⁺ → ATP demand**: Each Ca²⁺ ion requires 1 ATP for extrusion
- **Ca²⁺ → ATP production**: Mitochondrial Ca²⁺ stimulates TCA cycle
- **ATP → Ca²⁺ handling**: ATP fuels pumps, buffers, organelle uptake

### **Ca²⁺ ↔ BDNF (Trophic Loop)**

```
Presynaptic: Ca²⁺ influx → Vesicle release → Glutamate
Postsynaptic: Glutamate → NMDA → Ca²⁺ → BDNF synthesis
Retrograde: BDNF → Presynaptic TrkB → Enhanced Ca²⁺ signals
```

### **Ca²⁺ ↔ eCB (Retrograde Modulation)**

```
Postsynaptic: Ca²⁺ + mGluR → DAG → 2-AG synthesis
Retrograde: eCB → Presynaptic CB1 → Inhibits VGCC
Feedback: Reduced Ca²⁺ → Less glutamate → Less eCB
```

### **Ca²⁺ ↔ Lactate (Metabolic Feedback)**

```
Presynaptic Ca²⁺ → Glutamate release → Astrocyte uptake
Astrocyte: Glutamate → Na⁺ influx → Glycolysis → Lactate
Lactate → Presynaptic → ATP → Supports Ca²⁺ handling
```

### **Ca²⁺ ↔ K⁺/KChannels (Excitability Control)**

```
Ca²⁺ → SK channels → K⁺ efflux → Fast AHP → Limits firing
K⁺ accumulation → Depolarization → More VGCC opening → More Ca²⁺
Ca²⁺ → BK channels → Faster repolarization → Shorter AP
```

## **Ca²⁺-Dependent Plasticity Rules**

### **Short-term Rules (ms-s):**

```
Residual Ca²⁺ model: RRP release ∝ [Ca²⁺]_residual^n
Facilitation: PPR = 1 + ([Ca²⁺]_residual/EC₅₀) 
Depression: Vesicle depletion rate ∝ [Ca²⁺]_peak
```

### **Long-term Rules (min-days):**

```
BCM-like rule: 
  if [Ca²⁺]_avg < θ₁ → Downscale (LTD)
  if θ₁ < [Ca²⁺]_avg < θ₂ → No change
  if [Ca²⁺]_avg > θ₂ → Upscale (LTP)
  
θ₁ and θ₂ adjust based on Ca²⁺ history (metaplasticity)
```

### **Structural Rules:**

```
VGCC expression rate = k₁·[Ca²⁺]_integral - k₂·[VGCC]
RP size = k₃·BDNF·[Ca²⁺]_avg - k₄·[RP]
Where BDNF itself depends on Ca²⁺ history
```

## **Clinical/Experimental Implications**

### **Ca²⁺ Dysregulation Pathologies:**

- **Excitotoxicity**: Chronic high Ca²⁺ → mitochondrial failure → cell death
- **Synaptic fatigue**: Impaired Ca²⁺ clearance → reduced dynamic range
- **Plasticity disorders**: Altered Ca²⁺ setpoints → LTP/LTD imbalance

### **Measurement Approaches:**

- **Fast dyes (Fluo-4FF)**: Microdomain Ca²⁺ (ms)
- **GCaMP variants**: Global Ca²⁺ (10-100 ms resolution)
- **Ca²⁺ integrators (CaMKII)**: History over minutes
- **Structural readouts**: VGCC clustering, vesicle pools (hours-days)

### **Therapeutic Targets:**

- **VGCC blockers**: Reduce pathological Ca²⁺ influx
- **Ca²⁺ buffer enhancers**: Improve clearance
- **Mitochondrial Ca²⁺ uptake**: Protect against excitotoxicity
- **Ca²⁺ setpoint modulators**: Restore homeostatic balance

## **Summary: Ca²⁺ as Multiscale Integrator**

**Microscale (ms):** Release trigger → Digital signal (vesicle fusion/no fusion)  
**Mesoscale (100ms):** Plasticity mediator → Analog signal (facilitation/depression)  
**Macroscale (min):** Metabolic regulator → Energy allocation signal  
**Macroscale (hours):** Structural organizer → Growth/retraction signal

**Key Principles:**

1. **Dual signaling**: Microdomain (fast, local) vs Global (slow, integrative)
2. **Timescale-specific effectors**: Different targets at different Ca²⁺ durations
3. **Bidirectional coupling**: Ca²⁺ influences everything, everything influences Ca²⁺
4. **Setpoint homeostasis**: Systems maintain optimal Ca²⁺ levels across timescales
5. **Memory encoding**: Ca²⁺ history changes future Ca²⁺ handling

**The Ca²⁺ Paradox:**
The same ion that triggers millisecond release also organizes day-scale structural changes, with no contradiction because:

- Different **concentrations** activate different effectors
- Different **durations** engage different signaling pathways
- Different **localizations** communicate different information
- Different **frequencies** encode different messages

Ca²⁺ is not just a signal—it's the alphabet of presynaptic communication, with its timing, amplitude, and location forming words, sentences, and stories across timescales.

---

---

---

# CDI

**Ca²⁺-dependent inactivation** is a rapid negative feedback mechanism where **VGCCs self-regulate** by closing more quickly when **Ca²⁺ ions** bind to specific sites on the channel itself. This happens within **milliseconds** of channel opening.

## **Sequence of Events:**

text

```
1. VGCC opens → Ca²⁺ influx through pore
2. Ca²⁺ binds to CaM already tethered to channel (microdomain Ca²⁺ ~10-100 μM)
3. Ca²⁺/CaM complex conformation change
4. Ca²⁺/CaM binds to IQ domain
5. Channel pore undergoes conformational change → CLOSES
6. Channel enters inactivated state (refractory to reopening)
```

**Timing:**

- **Onset**: Within 5-50 ms of channel opening
- **Full inactivation**: 100-300 ms
- **Recovery**: 100-1000 ms (requires Ca²⁺ unbinding)

## **Functional Significance in Presynapse**

### **Millisecond Timescale Effects:**

| Effect                           | Consequence                            |
|----------------------------------|----------------------------------------|
| **Shortens Ca²⁺ influx duration**    | Limits total Ca²⁺ per action potential |
| **Prevents Ca²⁺ overload**           | Protects against excitotoxicity        |
| **Filters high-frequency firing**    | Channels inactivate during trains      |
| **Shapes AP-evoked Ca²⁺ transients** | Determines Ca²⁺ waveform               |

### **Impact on Vesicle Release:**

text

```
Without CDI: Sustained Ca²⁺ influx → higher Pr, more vesicles released
With CDI: Brief Ca²⁺ influx → lower Pr, fewer vesicles released
CDI modulation: Alters release probability dynamically
```

### **Short-term Plasticity Implications:**

- **High-frequency trains**: CDI accumulates → less Ca²⁺ per AP → depression
- **Recovery between bursts**: CDI relief → restored Ca²⁺ influx → facilitation
- **Frequency filtering**: CDI acts as low-pass filter for presynaptic Ca²⁺ signals

## **CDI vs Other Inactivation Mechanisms**

### **Three Types of VGCC Inactivation:**

1. **Ca²⁺-dependent (CDI)** - Fast, Ca²⁺-mediated (\~50 ms)
2. **Voltage-dependent (VDI)** - Slower, voltage-sensor mediated (\~100-500 ms)
3. **G-protein mediated** - Slower, neurotransmitter modulation (\~100-1000 ms)

### **Presynaptic Dominance:**

- **Calcium channels in presynapse**: Primarily **CaV2.1 (P/Q-type)** and **CaV2.2 (N-type)**
- **CDI strength**: CaV2.1 > CaV2.2
- **Location specificity**: Active zone channels show strongest CDI

## **Modulation of CDI by other factors**

### **BDNF Modulation:**

text

```
BDNF → TrkB → PLCγ → DAG → PKC → phosphorylates VGCC
Result: ↓ CDI → prolonged Ca²⁺ influx → enhanced release
```

### **NO Modulation:**

text

```
NO → sGC → cGMP → PKG → phosphorylates CaM or VGCC
Result: ↑ CDI → shorter Ca²⁺ influx → reduced release
```

### **eCB Modulation:**

text

```
eCB → CB1 → Gβγ → binds VGCC directly
Result: Channel inhibition + ↑ CDI → strong suppression
```

### **ATP/Energy Status:**

text

```
Low ATP → impaired Ca²⁺ pumps → elevated resting Ca²⁺
Result: CaM partially occupied → reduced CDI dynamic range
```