Local Glutamate-Glutamine Cycling Underlies Presynaptic ATP Homeostasis

Overview

This repository contains computational models and XPPAUT simulation files associated with the 2026 paper "Local Glutamate-Glutamine Cycling Underlies Presynaptic ATP Homeostasis" by Reinoud Maex, University of Hertfordshire, UK.

Simulation Files

All simulations are implemented in XPPAUT (XPP) format, a tool for solving differential equations and dynamical systems analysis developed by Bard Ermentrout.

Figure 3 Simulations

Figure3black.ode

Plain Model (Full Model)

Implements the complete plain model from Table 3 (Equations 1 and 2) of the paper. This is the main model featuring:

• Both glutamate (Glu) and ATP dynamics
• Workload-dependent glutamine uptake
• Activity-dependent ATP consumption
• Produces the black traces in Figure 3

Key features:

• Models both Glu' and ATP' differential equations
• Workload (w) modulates glutamine uptake: w * k11/k12 * orthoP^2 * Gln
• Left column: Workload increase from 1 to 2 (t=10 to 60)
• Right column: Workload decrease to 0.2 (commented out by default)

Figure3blue.ode

Variant II - Constant Glutamate

Implements model Variant II from Table 3, where:

• Cytosolic glutamate concentration is held constant at 1 mM
• Only ATP dynamics are modeled (Equation 2)
• Produces the blue traces in Figure 3

Key difference:

• Glu is a parameter, not a dynamic variable
• Demonstrates ATP homeostasis without dynamic glutamate regulation

Figure3green.ode

Variant I - Unity Omega

Implements model Variant I from Table 3, which is:

• Identical to the full model (black traces)
• Except omega (workload factor) is set to unity in Equations 1 and 2
• Produces the green traces in Figure 3

Key difference:

• Workload modulation removed from glutamine uptake: k11/k12 * orthoP^2 * Gln (no w factor)
• Shows importance of activity-dependent glutamine supply

Figure 4 Simulation

Figure4red.ode

Modified Model - Enhanced Glutamate Cycling

Implements a modified version of the plain model where:

• Parameter κ₂ (kappa2) is multiplied by 4
• Model is recalibrated accordingly
• Produces the red traces in Figure 4

Key modifications:

• k21 = 4 (instead of 1), enhancing the rate constant for glutamate-related processes
• Uses recalibrated expressions for κ₁ and κ₃ from Equations 6
• Demonstrates faster ATP homeostasis with increased glutamate cycling fraction
• Longer simulation time (220 time units vs 120)

Model Components

State Variables

• Glu: Cytosolic glutamate concentration (mM)
• ATP: Cytosolic ATP concentration (mM)

Static Variables

• orthoP: Inorganic phosphate (Pi), calculated as 0.2 * (9 - ATP)
• ADP: Adenosine diphosphate, equals orthoP in this model

Parameters

Constants (Table 1):

• Pyr: Pyruvate concentration = 0.04 mM
• Gln: Glutamine concentration = 0.4 mM

Free Parameters (Equations 8):

• k11, k12: Glutamine uptake rate constants (k11=1, k12=18.3)
• k21, k22: Glutamate vesicular accumulation rate constants (k21=1 or 4, k22=30.5)
• k31, k32: ATP production via Krebs cycle rate constants (k31=800, k32=30.5)

Key Processes Modeled

1. Glutamine Uptake and Conversion: Activity-dependent supply of glutamine by astrocytes
2. Glutamate Vesicular Accumulation: ATP-consuming process of packaging glutamate
3. ATP Production: Via Krebs cycle, dependent on glutamate conversion to α-ketoglutarate
4. ATP Consumption: Workload-dependent baseline consumption and glutamate packaging

Running the Simulations

Prerequisites

• Install XPPAUT

Modifying Workload

Each file includes commented lines to switch between workload conditions:

# For left column of Figure 3 (workload increase):
w = 1 + rect_pulse(t,10,60,1.0)

# For right column (workload decrease):
# w = 1 + rect_pulse(t,10,60,-0.8)

Uncomment the desired workload configuration to reproduce different figure panels.

Auxiliary Variables for Analysis

All models track:

• auxw: Workload over time
• ATPprod: Rate of ATP production
• ATPves: Rate of ATP consumption for glutamate vesicular packaging
• Gluprod: Rate of glutamate production

These can be plotted to analyze metabolic fluxes.

Key Findings

• ATP homeostasis is achieved through the balance of activity-dependent glutamine supply and glutamate accumulation/release
• The fraction of ATP spent on glutamate release and recycling is 4.7%, independent of workload
• Increasing this fraction (Figure 4) enhances the speed of ATP homeostasis and reduces futile ATP production
• The mechanism may be universal for axons releasing different neurotransmitters

Citation

If you use these models in your research, please cite:

Maex R. Local Glutamate-Glutamine Cycling Underlies Presynaptic ATP Homeostasis. Neural Comput. 2026 Feb 27;38(3):403-438. doi: 10.1162/NECO.a.1490. PMID: 41637722.