A biophysically grounded model of glutamatergic synaptic transmission integrating glutamate transport, receptor kinetics, and electrotonic effects.
The 3 matches
- [1] § Methods › Mathematical model › Glutamate transport ↔ Pars_and_Functions10_numba.py, lines 248–297 · score 0.55 · EAAT uptake, pulse, diffusion, duration, cleft, EAAT2
- [2] § Methods › Numerical implementation ↔ EAAT_main10.py, lines 816–860 · score 0.52 · Nelder Mead, error, minimizing, fitting
- [3] § Methods › Numerical implementation ↔ EAAT_main11.py, lines 832–876 · score 0.52 · Nelder Mead, error, minimizing, fitting
Paper
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The authors' code
Python · 434 lines · 16 KB · no license · 1 match
- import numpy as np
- import matplotlib.pyplot as plt
- from numba import njit
- def LoadExpData():
- # control AMPA current
- I_Exp_AMPA_con = []
- t_Exp_AMPA_con = []
- with open('control_copy.atf', 'r') as aaa:
- n = 0
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, I_contr = map(float, line.split()) # Assuming the file contains two floating-point numbers per line
- I_Exp_AMPA_con.append(I_contr * 1000)
- t_Exp_AMPA_con.append(ts * 1000 - 200) # ms
- n += 1
- # TBOA AMPA current
- I_Exp_AMPA_TBOA = []
- t_Exp_AMPA_TBOA = []
- with open('tboa_70_nM.atf', 'r') as aaa:
- n = 0
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, I_contr = map(float, line.split())
- I_Exp_AMPA_TBOA.append(I_contr * 1000)
- t_Exp_AMPA_TBOA.append(ts * 1000 - 200) # ms
- n += 1
- # TBOA, NMDA current, +40 and -40
- t_Exp_NMDA_TBOA = []
- I_Exp_NMDA_TBOA_plus40 = []
- I_Exp_NMDA_TBOA_min40 = []
- with open('2019-12-18_001Group1Series19.atf', 'r') as aaa:
- for i in range(10): # skip 10 lines of a header
- aaa.readline()
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, I_min40, dum1, dum2, I_plus40, dum3, dum4 = map(float, line.split())
- t_Exp_NMDA_TBOA.append(ts * 1000 - 1000) # ms
- I_Exp_NMDA_TBOA_plus40.append(I_plus40 * 1000)
- I_Exp_NMDA_TBOA_min40.append(I_min40 * 1000 + 270)
- # con, NMDA current, +40 and -40
- t_Exp_NMDA = []
- I_Exp_NMDA_plus40 = []
- I_Exp_NMDA_min40 = []
- with open('2019-12-02_001Group1Series04.atf', 'r') as aaa:
- for i in range(10): # skip 10 lines of a header
- aaa.readline()
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, I_min40, dum1, dum2, I_plus40, dum3, dum4 = map(float, line.split())
- t_Exp_NMDA.append(ts * 1000 - 1000) # ms
- I_Exp_NMDA_plus40.append(I_plus40 * 1000 - 300)
- I_Exp_NMDA_min40.append(I_min40 * 1000 + 80)
- # control CC
- V_Exp_CC = []
- t_Exp_CC = []
- with open('2018-11-16_001Group1Series8_CC_av.atf', 'r') as aaa:
- for i in range(10): # skip 10 lines of a header
- aaa.readline()
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, V_contr, dum1, dum2 = map(float, line.split())
- t0 = 0.152 # s start of response
- if ts >= t0:
- V_Exp_CC.append(V_contr - 6.3)
- t_Exp_CC.append((ts - t0) * 1000) # ms
- t_Exp_CC = np.array(t_Exp_CC)
- V_Exp_CC = np.array(V_Exp_CC)
- # control VC
- I_Exp_VC = []
- t_Exp_VC = []
- with open('2018-11-16_001Group1Series9_VC_av.atf', 'r') as aaa:
- for i in range(10): # skip 10 lines of a header
- aaa.readline()
- while True:
- line = aaa.readline()
- if not line: # End of file
- break
- ts, I_contr, dum1, dum2 = map(float, line.split())
- t0 = 0.152 # s start of response
- if ts >= t0:
- I_Exp_VC.append(I_contr * 1000 + 160)
- t_Exp_VC.append((ts - t0) * 1000) # ms
- t_Exp_VC = np.array(t_Exp_VC)
- I_Exp_VC = np.array(I_Exp_VC)
- I_Exp_VC = Filter_Array(I_Exp_VC, gam=0.2)
- return t_Exp_AMPA_con, I_Exp_AMPA_con, \
- t_Exp_AMPA_TBOA, I_Exp_AMPA_TBOA, \
- t_Exp_CC, V_Exp_CC, t_Exp_VC, I_Exp_VC, \
- t_Exp_NMDA_TBOA, I_Exp_NMDA_TBOA_plus40, I_Exp_NMDA_TBOA_min40, \
- t_Exp_NMDA, I_Exp_NMDA_plus40, I_Exp_NMDA_min40
- # ---------------------------------------------------------------------------
- # Stimulus functions
- # NOTE: These cannot be @njit because they are called from outside numba context
- # too, but Stim_5_njit below is the version used inside System_of_ODEs_njit.
- # ---------------------------------------------------------------------------
- def Stim(t, t0, duration):
- y = 0
- if (t >= t0) and (t <= t0 + duration):
- y = 1
- return y
- def Stim_5(t, t0, duration, ISI):
- y = 0
- iStim_ = int((t - t0) / ISI)
- if (iStim_ <= 4) and (t - t0 >= iStim_ * ISI) and (t - t0 <= iStim_ * ISI + duration):
- y = 1
- return y
- def Stim_5_100Hz(t, t0, duration):
- ISI_ = 10 # ms
- y = 0
- iStim_ = int((t - t0) / ISI_)
- if (iStim_ <= 4) and (t - t0 >= iStim_ * ISI_) and (t - t0 <= iStim_ * ISI_ + duration):
- y = 1
- return y
- # ---------------------------------------------------------------------------
- # numba-compatible version of the stimulus (no external calls, pure arithmetic)
- # ---------------------------------------------------------------------------
- @njit(cache=True)
- def Stim_5_njit(t, t0, duration, ISI):
- """Numba-compiled 5-pulse stimulus. Identical logic to Stim_5."""
- if ISI <= 0.0:
- return 0.0
- dt = t - t0
- if dt < 0.0:
- return 0.0
- iStim_ = int(dt / ISI)
- if iStim_ > 4:
- return 0.0
- t_in_pulse = dt - iStim_ * ISI
- if 0.0 <= t_in_pulse <= duration:
- return 1.0
- return 0.0
- # ---------------------------------------------------------------------------
- # Activation / transport functions — scalar versions for use inside @njit
- # ---------------------------------------------------------------------------
- @njit(cache=True)
- def S_AMPA_scalar(x):
- """Hill function for AMPA receptor sensitivity (eq. 11).
- EC50 = 1000 µM, Hill coefficient n = 1.6."""
- if x <= 0.0:
- return 0.0
- EC50 = 1000.0 # µM
- n = 1.6
- return 1.0 / (1.0 + (EC50 / x) ** n)
- @njit(cache=True)
- def S_NMDA_scalar(x):
- """Hill function for NMDA receptor sensitivity (eq. 11).
- EC50 = 4.7 µM, Hill coefficient n = 1."""
- if x <= 0.0:
- return 0.0
- EC50 = 4.7 # µM
- # n = 1 → 1/(1 + EC50/x)
- return 1.0 / (1.0 + EC50 / x)
- @njit(cache=True)
- def fEAAT2_scalar(glU, Na_e=130.0, Na_a=15.0):
- """EAAT2 transport function (eq. 14).
- k_half^Glu = 28 µM (same constant used in dF/dt and dD/dt)."""
- dNa = Na_e - Na_a
- k_ = dNa ** 1.5 / (50.0 ** 1.5 + dNa ** 1.5)
- return k_ * glU / (28.0 + glU)
- # ---------------------------------------------------------------------------
- # Array versions kept for post-processing / plotting (unchanged behaviour)
- # ---------------------------------------------------------------------------
- def S_AMPA(x):
- EC502 = 1000 # µM
- n22 = 1.6
- result = np.zeros_like(x)
- mask = x > 0
- result[mask] = 1.0 / (1.0 + (EC502 / x[mask]) ** n22)
- return result
- def S_NMDA(x):
- EC501 = 4.7 # µM
- n11 = 1
- result = np.zeros_like(x)
- mask = x > 0
- result[mask] = 1.0 / (1.0 + (EC501 / x[mask]) ** n11)
- return result
- def fEAAT2(glU, Na_e=130, Na_a=15):
- k_ = (Na_e - Na_a) ** 1.5 / (50 ** 1.5 + (Na_e - Na_a) ** 1.5)
- return k_ * glU / (28 + glU)
- def fNMDA(U, Mg=1):
- return 1.0 / (1.0 + (Mg / 3.57) * np.exp(-0.062 * U))
- # ---------------------------------------------------------------------------
- # Core ODE right-hand side — numba JIT compiled
- #
- # Paper equations implemented here:
- # eq.12 dC_glu/dt = (C_glu_periph - C_glu)/tau_glU + F*D*nu
- # eq.13 dC_glu_periph/dt = (C_glu - C_glu_periph)/(beta*tau_glU)
- # - C_glu_periph/tau_diff
- # - alpha_periph * f_EAAT2(C_glu_periph)
- # eq.15 dF/dt = (F0 - F)/tau_F + H_F*(1-F)*C_glu_periph/k_half
- # eq.16 dD/dt = (1-D)/tau_D - H_D*D*C_glu_periph/k_half
- # NOTE: sign of H_D term is negative (depression), matching eq.16
- # of the paper. The original code had the same sign convention
- # via H_D being defined as a positive number subtracted implicitly
- # through the "-" in the formula; here it is made explicit.
- # eq.9 d(mAMPA)/dt = (-mAMPA + S_AMPA(C_glu)) / tau_AMPA
- #
- # Consistency fix applied vs. original code:
- # * eq.13 second (sink) term: paper uses C_glu_periph/tau_diff,
- # original code used (glU0 - glU_perif)/tau_diff which adds a nonzero
- # baseline glU0. The numba version retains glU0 as a parameter to
- # preserve the original behaviour; a comment marks the discrepancy.
- # * k_half = 28 µM is hard-coded in the original; made explicit here.
- # ---------------------------------------------------------------------------
- @njit(cache=True)
- def System_of_ODEs_njit(t, y,
- t0, duration, amplitude, ISI,
- beta, tau_glU, tau_diff, glU0,
- alpha_periph,
- tau_F, H_F, F0,
- tau_AMPA,
- H_D, tau_D):
- """
- Numba-JIT right-hand side for the 5-ODE glutamate/plasticity system.
- State vector y = [C_glu, C_glu_periph, F, D, mAMPA]
- Parameters (all floats):
- t0, duration, amplitude, ISI – stimulus parameters
- beta – volume ratio (periph/cleft), eq.13
- tau_glU – cleft-to-periph diffusion time [ms], eqs.12,13
- tau_diff – periph-to-bath diffusion time [ms], eq.13
- glU0 – residual periph glutamate baseline [µM]
- (NOTE: paper eq.13 uses C_glu_periph/tau_diff,
- code uses (glU0 - C_glu_periph)/tau_diff;
- glU0=0 recovers the paper formula exactly)
- alpha_periph – EAAT uptake rate [µM/ms], eq.13
- tau_F, H_F, F0 – facilitation parameters, eq.15
- tau_AMPA – AMPA closing time [ms], eq.9
- H_D, tau_D – depression parameters, eq.16
- """
- C_glu = y[0]
- C_glu_periph = y[1]
- F = y[2]
- D = y[3]
- mAMPA = y[4]
- k_half = 28.0 # µM (half-max concentration for EAAT2 and plasticity scaling)
- # Stimulus pulse (eq.12, release term)
- nu_ = amplitude * Stim_5_njit(t, t0, duration, ISI)
- # eq.12: dC_glu/dt
- dglU_dt = (C_glu_periph - C_glu) / tau_glU + F * nu_ #* D # 12.03.2026
- # eq.13: dC_glu_periph/dt
- dglU_periph_dt = ((C_glu - C_glu_periph) / (tau_glU * beta)
- + (glU0 - C_glu_periph) / tau_diff
- - alpha_periph * fEAAT2_scalar(C_glu_periph))
- # eq.15: dF/dt
- dF_dt = -(F - F0) / tau_F + H_F * (1.0 - F) * C_glu_periph / k_half
- # eq.16: dD/dt
- dD_dt = -(D - 1.0) / tau_D - H_D * D * S_AMPA_scalar(C_glu) #* C_glu_periph / k_half # 12.03.2026
- # eq.9: d(mAMPA)/dt
- dmAMPA_dt = (-mAMPA + S_AMPA_scalar(C_glu) * D) / tau_AMPA # 12.03.2026
- return (dglU_dt, dglU_periph_dt, dF_dt, dD_dt, dmAMPA_dt)
- # #*******************************************************************************************************************
- # dglU_dt = (glU_perif - glU) / tau_glU + F_*nu_#*D #- EAAT *fEAAT2(glU, Na_e,Na_a)
- # dglU_perif_dt = (glU - glU_perif) / (tau_glU * beta) + (glU0 - glU_perif) / tau_diff - EAAT_perif*fEAAT2(glU_perif)
- # dF_dt = -(F-F0)/tau_F + H_F * (1-F) * glU_perif/28#muM
- # dD_dt = -(D- 1)/tau_D - H_D * D * S_AMPA(glU)
- # dmAMPA_dt = (- mAMPA + S_AMPA(glU) * D )/tau_AMPA
- # #*******************************************************************************************************************
- # ---------------------------------------------------------------------------
- # scipy-compatible wrapper (scipy passes (t, y) for solve_ivp, (y, t) for odeint)
- # Provide both flavours so the main script can choose freely.
- # ---------------------------------------------------------------------------
- def System_of_ODEs_ivp(t, y, t0, duration, amplitude, ISI, params):
- """Wrapper for scipy.integrate.solve_ivp (t, y) calling convention.
- Returns a list so it is drop-in compatible with the original function."""
- beta, tau_glU, tau_diff, glU0, alpha_periph, tau_F, H_F, F0, tau_AMPA, H_D, tau_D = params
- res = System_of_ODEs_njit(t, np.asarray(y, dtype=np.float64),
- t0, duration, amplitude, ISI,
- beta, tau_glU, tau_diff, glU0,
- alpha_periph,
- tau_F, H_F, F0,
- tau_AMPA,
- H_D, tau_D)
- return list(res)
- def System_of_ODEs(y, t, Stim_unused, t0, duration, amplitude, ISI, params):
- """Wrapper for scipy.integrate.odeint (y, t) calling convention.
- Signature is backward-compatible with the original EAAT_main66.py.
- The 'Stim_unused' argument is accepted but ignored (stimulus is
- recomputed inside the numba kernel via Stim_5_njit)."""
- beta, tau_glU, tau_diff, glU0, alpha_periph, tau_F, H_F, F0, tau_AMPA, H_D, tau_D = params
- res = System_of_ODEs_njit(t, np.asarray(y, dtype=np.float64),
- t0, duration, amplitude, ISI,
- beta, tau_glU, tau_diff, glU0,
- alpha_periph,
- tau_F, H_F, F0,
- tau_AMPA,
- H_D, tau_D)
- return list(res)
- # ---------------------------------------------------------------------------
- # Remaining utility functions — unchanged
- # ---------------------------------------------------------------------------
- def f_tau_diff(tau_diff0, d_tau_diff_dV, Vh):
- y = tau_diff0 + d_tau_diff_dV * (Vh + 66)
- if y < 10:
- y = 10
- return y
- def Filter_Array(x, gam=0.1):
- y = np.copy(x)
- for i in range(len(x) - 2, 0, -1):
- y[i] = y[i + 1] * (1 - gam) + gam * x[i]
- for i in range(1, len(x) - 1):
- y[i] = y[i - 1] * (1 - gam) + gam * y[i]
- return y
- def sigmoid(x):
- return 1.0 / (1.0 + np.exp(-x))
- def half_sigmoid(x):
- return 2.0 / (1.0 + np.exp(-x * 2)) - 1.0
- def Interpolate_for_t(tE, yE, t_):
- for i in range(len(tE)):
- if tE[i] >= t_:
- break
- return yE[i]
- def Residual(tE, yE, t, y, tend):
- Err = 0
- n = 0
- for i in range(len(t)):
- if (t[i] > 0) and (t[i] <= tend):
- n = n + 1
- yEi = Interpolate_for_t(tE, yE, t[i])
- Err = Err * (n - 1) / n + (y[i] - yEi) ** 2 / n
- return Err
- # ---------------------------------------------------------------------------
- # Trigger numba JIT compilation on import so the first solve_ivp/odeint call
- # does not pay the compilation cost.
- # ---------------------------------------------------------------------------
- def _warmup_numba():
- _y0 = np.array([0.0, 0.0, 0.5, 1.0, 0.0])
- _p = (50.0, 3.0, 1500.0, 0.01, 0.25, 3000.0, 10.0, 0.5, 4.0, 0.07, 100.0)
- System_of_ODEs_njit(0.0, _y0, 2.0, 1.0, 35.0, 20.0, *_p)
- System_of_ODEs_njit(3.0, _y0, 2.0, 1.0, 35.0, 20.0, *_p)
- _warmup_numba()
- # ---------------------------------------------------------------------------
- # Plotting S_AMPA, S_NMDA, fNMDA (unchanged from original)
- # ---------------------------------------------------------------------------
- plt.figure(figsize=(8, 5))
- x = np.logspace(-2, 5, num=80)
- Sampa = S_AMPA(x)
- Snmda = S_NMDA(x)
- fEAAT_arr = np.array([fEAAT2(xi) for xi in x])
- plt.subplot(211)
- plt.semilogx(x, Sampa, 'r-', label='S_AMPA(glU)')
- plt.semilogx(x, Snmda, 'orange', label='S_NMDA(glU)')
- plt.semilogx(x, fEAAT_arr, 'blue', label='f_EAAT(glU)')
- plt.title('Sigmoids')
- plt.xlabel('Glutamate, µM')
- plt.ylabel('Receptor activation')
- plt.grid(True)
- plt.legend()
- x2 = np.linspace(-80, 40, num=80)
- fnmda_arr = fNMDA(x2, 1)
- plt.subplot(212)
- plt.plot(x2, fnmda_arr, 'red', label='f_NMDA(U)')
- plt.title('f_NMDA for [Mg]_o = 1 mM')
- plt.xlabel('mV')
- plt.ylabel('units')
- plt.grid(True)
- plt.legend()
- plt.tight_layout()
- plt.savefig('Sigmoids.png', dpi=300)
Pars_and_Functions10_numba.py at commit 8fa8f6a, no license · at the source
Overview
- Computational Neurophysics Laboratory, Institute for Theoretical Physics, University of Bremen, Bibliothekstrasse 1, 28359 Bremen, Germany
- Sechenov Institute of Evolutionary Physiology and Biochemistry, Saint Petersburg, Russia
- Quantum Brains, Meraba Aleksidze street 12, 0171 Tbilisi, Georgia
Abstract
Gluatamatergic synaptic transmission, critical for learning and memory, relies on precise regulation of extracellular glutamate levels by astrocytic transporters, particularly EAAT2. While existing models of AMPA and NMDA receptor kinetics often oversimplify glutamate dynamics or become computationally intractable, this study develops a balanced, biophysically grounded model that integrates glutamate transport, receptor sensitivity, and electrotonic effects. Using rat hippocampal slices, we recorded postsynaptic currents in CA1 pyramidal neurons under control conditions and during glutamate transporter blockade. The proposed mathematical model, formulated as a system of seven ordinary differential equations, distinguishes somatic and dendritic compartments, synaptic plasticity, and differential glutamate sensitivity of AMPA and NMDA receptors. Key findings reveal that the glutamate transporter blockade prolongs NMDA receptor-mediated currents without altering AMPA receptor kinetics, consistent with the higher glutamate sensitivity of NMDA receptors. The model also predicts glutamate concentrations in synaptic and extrasynaptic spaces, offering insights into spatial neurotransmitter dynamics. Furthermore, it accounts for voltage-dependent NMDA responses and short-term plasticity observed experimentally. By bridging the gap between oversimplified and overly complex approaches, this work provides a versatile tool for studying synaptic transmission in normal and pathological conditions, such as epilepsy or neurodegenerative diseases, where glutamate dysregulation plays a central role.
Reproduced under the paper's license (CC BY), from the paper cited above.
Repository
Its files are read in the Code ↔ Paper reader above, with 3 matches between paragraphs and lines of code.
antonvchizhov/EAAT-paper
8fa8f6ac5340ed0ac3a01a8a987049d87b6aa617, 8 April 2026Availability: 1 check, the latest on 28 September 2026: the link answers
- 28 September 2026: the link answers
5 files
- EAAT_main10.py, Python, 860 lines, 1 match
- EAAT_main11.py, Python, 876 lines, 1 match
- Pars_and_Functions10_num
ba.py , Python, 434 lines, 1 match - Pars_and_Functions11_num
ba.py , Python, 404 lines - README.md, Text, 211 lines
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
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Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
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- Publisher: n/a → Springer Science+Business Media
Version 1, 28 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 7 keywords, 13 MeSH terms, 1 funder, 37 references.
Cite
This paper
Chizhov, A. V., Malkin, S. L., Khachatryan, D. N., & Zaitsev, A. V. (2026). A biophysically grounded model of glutamatergic synaptic transmission integrating glutamate transport, receptor kinetics, and electrotonic effects. Journal of computational neuroscience, 54(2), 393-406. https://
BibTeX
@article{chizhov2026biop
author = {Chizhov, A V and Malkin, S L and Khachatryan, D N and Zaitsev, A V},
title = {{A biophysically grounded model of glutamatergic synaptic transmission integrating glutamate transport, receptor kinetics, and electrotonic effects}},
journal = {Journal of computational neuroscience},
year = {2026},
month = may,
volume = {54},
number = {2},
pages = {393--406},
publisher = {Springer Science+Business Media},
issn = {0929-5313},
doi = {10.1007/
url = {https://
pmid = {42126468},
pmcid = {PMC13233636}
}
RIS
TY - JOUR
AU - Chizhov, A V
AU - Malkin, S L
AU - Khachatryan, D N
AU - Zaitsev, A V
TI - A biophysically grounded model of glutamatergic synaptic transmission integrating glutamate transport, receptor kinetics, and electrotonic effects
T2 - Journal of computational neuroscience
J2 - J Comput Neurosci
PY - 2026
DA - 2026/
VL - 54
IS - 2
SP - 393
EP - 406
SN - 0929-5313
PB - Springer Science+Business Media
DO - 10.1007/
UR - https://
LA - en
ER -
CSL-JSON
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}
}
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