Synapse Models Library

A comprehensive Rust library for modeling synaptic dynamics in computational neuroscience. This library provides detailed biophysical models of synaptic transmission, plasticity, and network dynamics.

Features

Neurotransmitter Dynamics

• Multiple neurotransmitter types: Glutamate, GABA, Dopamine, Serotonin, Acetylcholine, Norepinephrine
• Realistic kinetics: Exponential decay with biologically accurate time constants
• Diffusion and clearance: Based on experimental measurements

Receptor Models

• Ionotropic receptors: AMPA, NMDA, GABA-A with detailed kinetic schemes
• Metabotropic receptors: GABA-B, mGluR with G-protein coupling
• NMDA voltage dependence: Mg²⁺ block with Jahr & Stevens (1990) model
• Calcium permeability: NMDA-mediated Ca²⁺ influx

Vesicle Pool Dynamics

• Tsodyks-Markram model: Short-term depression and facilitation
• Multiple pools: Ready releasable, reserve, and recycling pools
• Calcium-dependent release: Hill equation with cooperativity
• Quantal release: Binomial statistics with multi-vesicular release

Calcium Dynamics

• Pre/postsynaptic compartments: Independent calcium dynamics
• Buffering: Fast and slow buffers with realistic binding kinetics
• Calcium stores: ER uptake/release with SERCA pumps
• CICR: Calcium-induced calcium release via RyR
• IP3 signaling: IP3 receptor-mediated release

Plasticity Rules

• STDP: Spike-timing dependent plasticity with asymmetric window
• BCM rule: Bienenstock-Cooper-Munro with sliding threshold
• Oja's rule: Normalized Hebbian learning
• Hebbian/Anti-Hebbian: Classic learning rules
• Homeostatic plasticity: Activity-dependent scaling
• Meta-plasticity: Plasticity of plasticity

Network Models

• Chemical synapses: Full models with delays and dynamics
• Gap junctions: Electrical synapses with bidirectional coupling
• Ephaptic coupling: Electric field effects
• Neuromodulation: Dopamine, serotonin, ACh, norepinephrine
• Spike propagation: Event-driven with realistic delays

Installation

Add to your Cargo.toml:

[dependencies]
synapse-models = "0.1.0"

Quick Start

Basic Synaptic Transmission

use synapse_models::Synapse;

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Create an excitatory synapse
    let mut synapse = Synapse::excitatory(1.0, 1.0)?;

    // Presynaptic spike
    synapse.presynaptic_spike(0.0)?;

    // Simulate for 10 ms
    for t in 0..100 {
        let time = t as f64 * 0.1;
        synapse.update(time, -65.0, 0.1)?;

        println!("t={:.1} ms, g={:.4} nS", time, synapse.conductance());
    }

    Ok(())
}

STDP Learning

use synapse_models::Synapse;

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut synapse = Synapse::excitatory(0.5, 1.0)?;
    let initial_weight = synapse.weight;

    // Pre before post (10 ms) → potentiation
    synapse.presynaptic_spike(0.0)?;
    synapse.postsynaptic_spike(10.0)?;

    println!("Weight change: {:.6}", synapse.weight - initial_weight);
    // Output: Weight change: 0.006065 (potentiation)

    Ok(())
}

Network Simulation

use synapse_models::{SynapticNetwork, Synapse};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Create a network with 10 neurons
    let mut network = SynapticNetwork::new(10);

    // Add connections
    for i in 0..9 {
        let syn = Synapse::excitatory(1.0, 2.0)?;
        network.add_connection(i, i + 1, syn)?;
    }

    // Spike from first neuron
    network.spike(0)?;

    // Simulate
    let voltages = vec![-65.0; 10];
    for _ in 0..100 {
        network.update(&voltages, 0.1)?;
    }

    // Get synaptic current to neuron 5
    let current = network.get_synaptic_current(5)?;
    println!("Current to neuron 5: {:.2} pA", current);

    Ok(())
}

Biophysical Parameters

All parameters are based on experimental data:

AMPA Receptors

• Rise time: 0.2 ms
• Decay time: 2 ms
• Reversal potential: 0 mV

NMDA Receptors

• Rise time: 2 ms
• Decay time: 100 ms
• Reversal potential: 0 mV
• Mg²⁺ block: Jahr & Stevens (1990)

GABA-A Receptors

• Rise time: 0.5 ms
• Decay time: 5 ms
• Reversal potential: -70 mV

GABA-B Receptors

• Rise time: 50 ms
• Decay time: 200 ms
• Reversal potential: -90 mV

Vesicle Pool (Tsodyks-Markram)

• Depressing: U = 0.6, τ_rec = 130 ms
• Facilitating: U = 0.15, τ_rec = 670 ms, τ_facil = 17 ms

STDP

• Potentiation window: τ+ = 20 ms, A+ = 0.01
• Depression window: τ- = 20 ms, A- = 0.01

Mathematical Models

Receptor Kinetics

First-order binding:

dR/dt = α[NT](1-R) - βR

where R is open probability, [NT] is neurotransmitter concentration.

NMDA Mg²⁺ Block

Jahr & Stevens (1990):

B(V) = 1 / (1 + [Mg²⁺]/3.57 * exp(-0.062*V))

Tsodyks-Markram Model

dx/dt = (1-x)/τ_rec - U*x*δ(t-t_spike)
du/dt = (U₀-u)/τ_facil + U₀(1-u)δ(t-t_spike)

STDP Window

Δw = A+ * exp(-Δt/τ+)     for Δt > 0 (potentiation)
Δw = -A- * exp(Δt/τ-)     for Δt < 0 (depression)

Examples

Run the examples:

# Basic synapse simulation
cargo run --example basic_synapse

# Network simulation
cargo run --example network_simulation

Testing

Run the comprehensive test suite:

cargo test --package synapse-models

All 68 tests cover:

• Neurotransmitter dynamics
• Receptor kinetics and voltage dependence
• Vesicle pool dynamics
• Calcium dynamics and CICR
• All plasticity rules
• Synapse integration
• Network connectivity and propagation

Performance

• Numerical integration: Exponential Euler for stability
• Sparse networks: Efficient adjacency list representation
• Thread-safe: Safe for parallel neuron updates
• Minimal allocations: Optimized for real-time simulation

Architecture

synapse-models/
├── src/
│   ├── lib.rs              # Main library with documentation
│   ├── error.rs            # Error types
│   ├── neurotransmitter.rs # Neurotransmitter dynamics
│   ├── receptor.rs         # Receptor models
│   ├── vesicle.rs          # Vesicle pool dynamics
│   ├── calcium.rs          # Calcium dynamics
│   ├── plasticity.rs       # Learning rules
│   ├── synapse.rs          # Complete synapse model
│   └── network.rs          # Network-level dynamics
├── examples/               # Example programs
└── tests/                  # Integration tests

References

Key Papers

1. Tsodyks & Markram (1997) - Short-term synaptic plasticity model

   • Proc Natl Acad Sci USA 94(2):719-723

2. Bi & Poo (1998) - STDP experimental characterization

   • J Neurosci 18(24):10464-10472

3. Jahr & Stevens (1990) - NMDA Mg²⁺ block

   • J Neurosci 10(6):1830-1837

4. Bienenstock et al. (1982) - BCM theory

   • J Neurosci 2(1):32-48

Textbooks

• Dayan & Abbott (2001) - Theoretical Neuroscience
• Gerstner et al. (2014) - Neuronal Dynamics
• Koch (1999) - Biophysics of Computation

Contributing

This library is part of the CORTEXIA computational neuroscience toolkit. Contributions are welcome!

License

MIT OR Apache-2.0

Authors

• Francisco Molina Burgos
• Claude-CORTEXIA

Citation

If you use this library in your research, please cite:

@software{synapse_models,
  title = {Synapse Models: A Comprehensive Rust Library for Synaptic Dynamics},
  author = {Molina Burgos, Francisco and Claude-CORTEXIA},
  year = {2024},
  url = {https://github.com/cortexia/synapse-models}
}

Acknowledgments

This library implements models from numerous experimental and theoretical studies in neuroscience. We thank the researchers whose work made this possible.