# 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](/2020506?tab=2&file=modelDB/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](/2020506?tab=2&file=modelDB/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](/2020506?tab=2&file=modelDB/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](/2020506?tab=2&file=modelDB/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](http://www.math.pitt.edu/~bard/xpp/xpp.html) ### Modifying Workload Each file includes commented lines to switch between workload conditions: ```c # 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](https://doi.org/10.1162/NECO.a.1490). [PMID: 41637722](https://pubmed.gov/41637722).