NMDA Receptor Kinetics Drive Distinct Routes to Chaotic Firing in Pyramidal Neurons

NMDA receptors, neuronal dynamics, synaptic plasticity, chaos theory, infor-30 mation theory, computational neuroscience, addiction, visual processing31 1 Introduction32 Information processing in the brain depends on precisely tuned interactions between intrinsic mem-33 brane conductances and synaptic receptor dynamics. NMDA receptors play a pivotal role in exci-34 tatory synaptic transmission, distinguished by their voltage-dependent Mg 2+ block and relatively35 slow deactivation kinetics Kampa et al. (2004); Vargas-Caballero and Robinson (2004). These36 characteristics mediate extended calcium influx into postsynaptic neurons, influencing long-term37 potentiation (LTP), long-term depression (LTD), and other plasticity-related processes L¨ uscher38 and Malenka (2012). Beyond synaptic plasticity, NMDA receptors modulate neuronal firing stabil-39 ity and variability, with direct consequences for information encoding and transmission Harsch and40 Robinson (2000); Hunt and Castillo (2012).41 A central question in computational neuroscience concerns how changes in NMDA receptor gat-42 ing kinetics—particularly closing rates (βN M DA) and glutamate stimulation frequencies—transition43 neurons between stable periodic firing and irregular chaotic regimes Durstewitz and Gabriel (2007);44 Soudry and Meir (2012). While irregular spiking can degrade information transfer reliability, it may45 also increase dynamic range and encoding flexibility de Ruyter van Steveninck et al. (1997); Ermen-46 trout et al. (2008). Despite extensive research on excitatory-inhibitory balance effects on neuronal47 dynamics, the detailed parameter space of NMDA receptor kinetics has received limited systematic48 investigation. The precise influence of NMDA receptor kinetics on plasticity induction, inter-spike49 interval (ISI) frequency band emergence, and their implications for single-cell information encoding50 remains incompletely understood.51 The clinical significance of NMDA receptor kinetic alterations extends across multiple neuropsy-52 chiatric conditions. In schizophrenia, altered receptor kinetics may contribute to gamma oscillation53 abnormalities and cognitive deficits Coyle (2012); Gandal et al. (2012). Autism spectrum disorders54 involve NMDA-mediated excitation-inhibition imbalances affecting sensory processing and social55 cognition Rubenstein and Merzenich (2003); Lee et al. (2017). Alzheimer’s disease features pro-56 gressive NMDA receptor dysfunction correlating with synaptic loss and memory impairment Wang57 and Reddy (2017); Snyder et al. (2005); Hynd et al. (2004). Chronic pain conditions exhibit altered58 NMDA kinetics in spinal cord circuits, contributing to central sensitization Latremoliere and Woolf59 (2009); Zhuo (2016).60 In addiction neuroscience, chronic substance exposure alters NMDA receptor expression and61 kinetics, contributing to pathological synaptic plasticity underlying addiction-related memory for-62 mation and relapse vulnerability Kalivas (2009); Wolf (2016). Pathological memory formation63 represents a critical mechanism underlying addiction persistence and relapse vulnerability. Unlike64 normal learning and memory, drug-induced memories exhibit abnormal persistence, resistance to65 extinction, and heightened salience that can trigger craving and relapse even after prolonged absti-66 nence Kalivas (2009); Wolf (2016). These pathological memories form through aberrant synaptic67 plasticity mechanisms involving dysregulated NMDA receptor function and downstream signaling68 cascades, particularly calcium-dependent processes such as CaMKII phosphorylation L¨ uscher and69 Malenka (2011); Pascoli et al. (2014).70 Previous computational modeling has demonstrated that opioid exposure fundamentally alters71 synaptic plasticity mechanisms through disruption of calcium homeostasis and CaMKII phosphory-72 lation dynamics Borjkhani et al. (2018a,b). These studies revealed that chronic drug exposure shifts73 2 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint the balance between LTP and LTD, favoring persistent synaptic modifications that encode drug-74 associated memories. NMDA receptors serve as critical gatekeepers in this process, with their kinetic75 properties determining calcium influx magnitude and persistence. Our research group has previ-76 ously developed computational frameworks demonstrating how opioids induce pathological memory77 formation through theta rhythm generation during chronic consumption (Borjkhani et al., 2018c),78 and how cocaine disrupts action potential generation by reducing potassium currents (Borjkhani79 et al., 2022). These studies established the foundation for investigating drug-induced alterations in80 neural dynamics and synaptic plasticity mechanisms.81 Evidence suggests NMDA receptor antagonists can disrupt drug memory reconsolidation and82 reduce relapse rates in preclinical studies Lee et al. (2006); Das et al. (2013). However, the precise83 relationship between NMDA receptor kinetic properties and pathological memory formation versus84 maintenance remains incompletely characterized. This knowledge gap represents a barrier to devel-85 oping targeted therapeutic interventions that could selectively disrupt maladaptive memories while86 preserving normal memory function.87 In visual neuroscience, NMDA receptors are essential for retinal ganglion cell function and88 cortical visual processing Manookin et al. (2010); Fox and Daw (1992). Receptor dysfunction con-89 tributes to glaucoma, diabetic retinopathy, and cortical visual impairment through altered firing90 patterns that disrupt normal visual processing Bai et al. (2013); Seki and Lipton (2008). In pri-91 mary visual cortex, NMDA receptors mediate orientation selectivity refinement, ocular dominance92 plasticity, and contrast adaptation mechanisms Morishita and Hensch (2008); Hensch (2005). The93 kinetic properties of these receptors directly influence critical period timing and the capacity for94 experience-dependent plasticity throughout life Hensch (2005).95 Recent evidence suggests altered NMDA kinetics contribute to visual processing deficits in neu-96 rodevelopmental disorders. In amblyopia, disrupted NMDA-dependent plasticity prevents normal97 binocular integration, while in autism spectrum disorders, altered excitation-inhibition balance af-98 fects visual motion processing and gamma oscillations Foss-Feig et al.(2013); Robertson and Baron-99 Cohen (2016). Age-related changes in NMDA receptor function may contribute to declining visual100 processing efficiency in older adults, with reduced NMDA-mediated plasticity affecting contrast101 sensitivity and temporal processing Hua et al. (2008).102 Here, we develop and analyze a single-compartment Hodgkin-Huxley-type model of a pyramidal103 neuron incorporating sodium, potassium, and calcium currents, along with GABAergic, AMPA, and104 NMDA synaptic conductances. Building upon our previous computational investigations of opioid-105 induced memory formation (Borjkhani et al., 2018c) and cocaine effects on neuronal excitability106 (Borjkhani et al., 2022), we extend this framework to systematically examine NMDA receptor107 kinetic control of cortical dynamics. We include CaMKII phosphorylation dynamics as a biochemical108 pathway linking calcium transients to synaptic plasticity. By systematically varying βN M DA and109 glutamatergic drive frequency, we evaluate how neuronal firing evolves through different oscillatory110 modes and assess impacts on spike-timing entropy, maximum Lyapunov exponent, and mutual111 information. We investigate how GABAergic inhibition modulates these transitions through fast112 inhibitory currents that control neuronal excitability and chaotic dynamics.113 Our findings reveal dual pathways to firing irregularity and establish NMDA receptor kinetics114 as fundamental controllers of cortical excitability and information processing. These results provide115 mechanistic insights into addiction-related memory disorders and visual processing dysfunction,116 suggesting therapeutic strategies targeting NMDA receptor kinetic normalization and oscillatory117 pattern restoration.118 3 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 2 Materials and Methods119 Figure 1 provides an overview of our comprehensive computational approach to investigating NMDA120 receptor kinetics and their control over neuronal dynamics. The workflow encompasses four in-121 tegrated stages: systematic model development and parameter space exploration, application of122 multiple dynamical analysis methods, identification of key mechanistic findings through the dual123 pathways framework, and translation to clinical applications. This systematic approach allows us124 to bridge molecular receptor properties with network-level dynamics and establish direct relevance125 to addiction neuroscience and visual processing disorders. The following sections detail each com-126 ponent of this workflow, beginning with the neuronal model architecture.127 2.1 Neuronal Model Overview128 For the simulation of a pyramidal neuron in the cortex, we employed a single-compartment Hodgkin-129 Huxley-type model based on Golomb et al. Golomb et al. (2006). The model was modified to130 incorporate glutamatergic and GABAergic receptors (NMDA, AMPA, and GABA receptors) along-131 side ionotropic channels, enabling responses to both excitatory and inhibitory neurotransmitters.132 Furthermore, the model incorporates CaMKII phosphorylation dynamics as a function of calcium133 concentration variations, providing a mechanistic link between synaptic activity and plasticity Bor-134 jkhani et al. (2018a). This computational framework allows investigation of NMDA receptor kinetics135 effects on neuronal excitability relevant to addiction-related plasticity mechanisms and visual pro-136 cessing disorders. Figure 2 shows the general structure of the modeled elements.137 2.1.1 Model Validation and Verification138 The model was validated against experimental data from pyramidal neurons in layers 2/3 of visual139 cortex Markram et al. (1997). Key validation metrics included: (1) resting potential (-65 ± 5 mV),140 (2) action potential amplitude (80-100 mV), (3) spike threshold (-45 ± 3 mV), and (4) adaptation141 ratio (0.6-0.8) during sustained current injection. Numerical integration was verified using analytical142 solutions for simplified cases and compared with NEURON simulator results (relative error< 0.1%).143 2.2 Membrane Dynamics144 The membrane potential ( V ) in the excitatory postsynaptic neuron is governed by the following145 differential equation:146 Cm ∂V ∂t = − (INa + INaP + IKdr + IA + IM + ICa + IC + IsAHP + IL + Isyn) (1) where the membrane capacitance Cm = 1 µF/cm2 and the total synaptic current is:147 Isyn = IAMPA + INMDA + IGABA (2) = gAMPAmAMPA(V − EAMPA) + gNMDAmNMDABMg(V )(V − ENMDA) + gGABAmGABA(V − EGABA) (3) 4 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 2.3 Intrinsic Ionic Currents148 2.3.1 Sodium Currents149 The transient sodium current is described by:150 INa = gNam3h(V − ENa) (4) where gNa = 35 mS/cm2 and ENa = 55 mV is the sodium reversal potential. The activation and151 inactivation gating variables are denoted by m = m∞(V ) and:152 dh dt = ϕ[h∞(V ) − h] τh(V ) (5) where ϕ = 5 is a temperature factor and the time constant is:153 τh(V ) = 0.1 + 0.75 · [1 + exp(−(V + 40.5)/(−6))]−1 ms (6) The persistent sodium current is:154 INaP(V ) = 0.1 · p∞(V ) · (V − 55) mS/cm2 (7) 2.3.2 Potassium Currents155 The delayed rectifier potassium current is:156 IKdr(V, n) = gKdrn4(V + 90) (8) where gKdr = 6 mS/cm2 is the default conductance. The gating variable n follows:157 dn dt = ϕ[n∞(V ) − n] τn(V ) (9) with time constant:158 τn(V ) = 0.1 + 0.5 · [1 + exp(−(V + 27)/(−15))]−1 ms (10) The A-type potassium current has the following dynamics:159 IA(V, b) = 1.4 · a2 ∞(V ) · b · (V + 90) mS/cm2 (11) where a = a∞(V ) and:160 db dt = b∞(V ) − b 15 ms (12) The muscarinic-sensitive potassium current is:161 IM(V, z) = 1 · z · (V + 90) mS/cm2 (13) with gating variable dynamics:162 dz dt = z∞(V ) − z 75 ms (14) 5 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 2.3.3 Calcium Currents163 The high-voltage calcium current is:164 ICa(V, r) = 0.2 · r2 · (V − 120) mS/cm2 (15) with gating variable:165 dr dt = r∞(V ) − r 1 ms (16) The fast calcium-activated potassium current is:166 IC(V, c) = 10 · d∞([Ca2+]i) · c · (V + 90) mS/cm2 (17) where [Ca2+]i is the intracellular calcium concentration, and:167 dc dt = c∞(V ) − c 3 ms (18) d∞([Ca2+]i) = [1 + 6/[Ca2+]i]−1 (19) The slow calcium-activated potassium current (afterhyperpolarization) is:168 IsAHP(V, q) = 5 · q · (V + 90) mS/cm2 (20) with gating variable dynamics:169 dq dt = q∞([Ca2+]i) − q 450 ms (21) q∞([Ca2+]i) = [1 + 24/[Ca2+]4 i ]−1 (22) 2.3.4 Leak Current170 The leak current is modeled as:171 IL = 0.05 · (V + 70) mS/cm2 (23) 2.4 Calcium Dynamics172 The intracellular calcium concentration evolves according to:173 d[Ca2+]i dt = −0.13ICa − 0.012INMDA − 0.0012IAMPA − [Ca2+]i 13 ms (24) This equation accounts for calcium influx through voltage-gated calcium channels, NMDA receptors,174 and AMPA receptors (to a lesser extent), as well as calcium extrusion and buffering mechanisms175 with a time constant of 13 ms.176 2.5 Synaptic Currents177 2.5.1 AMPA Receptors178 The AMPA-mediated current is calculated as:179 IAMPA = gAMPA · mAMPA · (V − EAMPA) (25) where gAMPA = 0.5 nS and EAMPA = 0 mV. The gating variable mAMPA follows:180 dmAMPA dt = αAMPA · Gglu(t) · (1 − mAMPA) − βAMPA · mAMPA (26) where αAMPA = 1.1 mM−1ms−1 and βAMPA = 0.67 ms−1 are the opening and closing rates, respec-181 tively. Gglu(t) represents the time-varying glutamate concentration that activates the receptor.182 6 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 2.5.2 NMDA Receptors183 The NMDA current is modeled as:184 INMDA = gNMDA · mNMDA · BMg(V ) · (V − ENMDA) (27) where gNMDA = 0.5 nS and ENMDA = 0 mV. The voltage-dependent Mg 2+ block is:185 BMg(V ) = 1 1 + [Mg2+]o 3.75 exp(−0.062V ) (28) where [Mg2+]o = 2 mM is the extracellular magnesium concentration.186 The NMDA receptor gating variable follows:187 dmNMDA dt = αNMDA · Gglu(t) · (1 − mNMDA) − βNMDA · mNMDA (29) where αNMDA = 0.14 mM−1ms−1 is the opening rate and βNMDA is the systematically varied closing188 rate (range: 0.01–0.1 ms −1). This parameter represents the key experimental variable in our study,189 as alterations in NMDA receptor kinetics are implicated in both addiction-related plasticity and190 visual processing disorders.191 2.5.3 GABA Receptors192 The GABAergic inhibitory current is:193 IGABA = gGABA · mGABA · (V − EGABA) (30) where gGABA = 1.0 nS and EGABA = −70 mV.194 The GABA receptor gating variable follows:195 dmGABA dt = αGABA · GGABA(t) · (1 − mGABA) − βGABA · mGABA (31) where αGABA = 2.0 mM−1ms−1 and βGABA = 1.5 ms−1.196 2.6 Activation Functions197 All steady-state activation and inactivation functions follow the standard Boltzmann form:198 x∞(V ) = [1 + exp(−(V − θx)/σx)]−1 (32) where x can be replaced by m, h, n, a, b, z, p, r, or c. The parameters are summarized in Table 1.199 2.7 CaMKII Phosphorylation Dynamics200 Postsynaptic Ca2+ concentration variations lead to CaMKII phosphorylation, which is governed by201 equations adapted from Borjkhani et al. Borjkhani et al. (2018a,b) and Zhabotinsky Zhabotinsky202 (2000):203 Ph.CaMKII = fCaMKII([Ca2+]i) (33) The detailed phosphorylation cascade involves 10 differential equations governing the concen-204 trations of i-fold phosphorylated CaMKII (P i, where i = 0, 1, ...,10). The system includes:205 7 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint Table 1: Gating Variable Parameters for Activation/Inactivation Functions Variable θ (mV) σ (mV) Source m -30 9.5 Golomb et al. (2006) h -45 -7 Golomb et al. (2006) n -35 10 Golomb et al. (2006) a -50 20 Golomb et al. (2006) b -80 -6 Golomb et al. (2006) z -39 5 Golomb et al. (2006) p -41 3 Golomb et al. (2006) r -20 10 Golomb et al. (2006) c -30 7 Golomb et al. (2006) Phosphorylation rates:206 v1 = 10k1([Ca2+]/KH1)8P0 (1 + ([Ca2+]/KH1)4)2 (34) v2 = k1([Ca2+]/KH1)4 1 + ([Ca2+]/KH1)4 (35) v3 = k2ep KM + P10 i=1 iPi (36) where k1 = 0.5 s−1 is the I1-dependent regulation rate of PP1, KH1 = 4 µM is the Hill constant207 of CaMKII for calcium activation, KM = 20 µM and k2 = 10 s−1 are the Michaelis and catalytic208 constants, respectively.209 Additional parameters:210 • ep: PP1 concentration not bound to I1P (active protein phosphatase)211 • ep0 = 0.1 µM: total PP1 concentration212 • I0 = 0.1 µM: free I1 concentration213 • k3 = 1 µM−1s−1 and k4 = 10 −3 s−1: association and dissociation rate constants of PP1-I1P214 complex215 • vCaN = 2 s−1: rate of I1P dephosphorylation due to calcineurin216 • vPKA = 0.45 µM/s: phosphorylation rate of I1 due to PKA217 • KH2 = 0.7 µM: calcium activation Hill constant of calcineurin218 The total phosphorylated CaMKII is:219 Ph.CaMKII = fCaMKII([Ca2+]i) = 10X i=1 Pi (37) CaMKII phosphorylation levels were recorded at each time step and correlated with ISI patterns220 to investigate plasticity-related dynamics relevant to addiction and visual processing mechanisms.221 8 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 2.8 Computational Implementation222 2.8.1 Software and Hardware Environment223 All simulations were implemented in Python 3.8.10 using NumPy 1.21.0, SciPy 1.7.0, and Mat-224 plotlib 3.4.2. Computations were performed on a high-performance computing cluster with Intel225 Xeon Gold 6248 processors (2.5 GHz, 40 cores) and 192 GB RAM. Parallel processing utilized the226 multiprocessing library with 20 worker processes. Total computational time was approximately 480227 CPU-hours.228 2.8.2 Numerical Integration and Simulation Parameters229 All simulations employed fourth-order Runge-Kutta integration with ∆ t = 0.05 ms, chosen based230 on convergence analysis showing < 0.1% error compared to ∆t = 0.01 ms. Simulation duration was231 10 seconds with the first 2 seconds discarded to eliminate transients, determined from pilot studies232 showing equilibration within 1.5 seconds.233 Glutamatergic stimulation consisted of 5 ms rectangular pulses with amplitude Gglu = 1 µM234 and frequencies ranging from 1–250 Hz (25 logarithmically spaced values). GABAergic stimulation,235 when present, provided continuous background inhibition at three levels: 0 Hz (control), 25 Hz, and236 50 Hz with GGABA = 0.5 µM.237 2.8.3 Parameter Space Exploration238 We systematically varied βNMDA across 20 logarithmically spaced values (0.01–0.1 ms −1) and stim-239 ulation frequency across 25 values (1–250 Hz), combined with 3 GABAergic conditions, generating240 1,500 unique parameter combinations (20 × 25 × 3). Each combination was replicated n = 10 times241 with different random seeds (using numpy.random with seeds 0–9), totaling 15,000 simulations and242 yielding 2,942,093 ISI observations after quality control.243 2.9 Data Analysis Pipeline244 2.9.1 Spike Detection and Quality Control245 Action potentials were detected using a dual-threshold algorithm: initial detection at V = 0 mV,246 confirmation at V = 20 mV, with a 2 ms absolute refractory period. Inter-spike intervals were247 calculated as:248 ISIi = ti+1 − ti (38) Quality control procedures excluded: (1) physiologically implausible ISIs ( 2000249 ms), (2) simulations with 200 mV). This resulted in exclusion of 1.2% of the total dataset.251 2.9.2 Dynamical Analysis Measures252 Shannon Entropy: ISI variability was quantified using 20 equal-width bins based on Sturges’ rule253 for the dataset size:254 H = − 20X k=1 pk log2 pk (39) where pk represents the probability of the k-th ISI bin. Bin width was determined individually for255 each parameter combination to ensure adequate sampling.256 9 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint Maximum Lyapunov Exponents: Estimated using the Wolf et al. (1985) algorithm Wolf257 et al. (1985) with embedding dimension d = 5, time delay τ = 5 ms (determined from first minimum258 of mutual information), and nearest neighbor radius r = 0.1 mV. Convergence was verified by259 requiring 0) indicate chaotic260 dynamics.261 Mutual Information: Calculated between parameters and ISI patterns using:262 MI(X; Y ) = X x,y p(x, y) log2 p(x, y) p(x)p(y) (40) Bias correction was applied using the Miller-Madow estimator Miller (1955). Statistical signifi-263 cance was assessed using surrogate data generated by 1000 random permutations.264 2.9.3 Frequency Band Classification265 ISIs were categorized into physiologically relevant bands based on inverse frequency relationships:266 gamma (7–33 ms, corresponding to 30–143 Hz), beta (33–77 ms, 13–30 Hz), alpha (77–125 ms, 8–13267 Hz), theta (125–250 ms, 4–8 Hz), and delta (250–2000 ms, 0.5–4 Hz). Probability density functions268 were estimated using Gaussian kernel density estimation with Scott’s rule for bandwidth selection.269 2.9.4 Bifurcation and Phase Space Analysis270 Bifurcation diagrams plotted steady-state ISI values against βNMDA after 2000 ms equilibration.271 Local maxima and minima were identified using a peak-finding algorithm with minimum prominence272 of 5% of the dynamic range. Phase portraits were constructed by plotting membrane voltage V (t)273 versus its numerical derivative dV /dt calculated using central differences.274 2.9.5 Statistical Analysis and Validation275

are presented as mean ± SEM across n = 10 replications. Statistical significance was276 assessed using two-way ANOVA ( α = 0 .05) with Bonferroni correction for multiple comparisons.277 Effect sizes are reported as partial eta-squared (η 2 p). Assumptions were tested using Shapiro-Wilk278 tests for normality and Levene’s test for homoscedasticity.279 Cross-validation was performed using 5-fold temporal splitting to assess stability of dynamical280 measures. Bootstrap confidence intervals (95%, n = 1000) were calculated for all summary statis-281 tics. Sensitivity analysis varied key parameters (integration timestep, bin numbers, embedding282 dimensions) by ±25% to ensure robustness of findings.283 2.10 Model Limitations284 The current model incorporates several simplifications: (1) single-compartment geometry neglect-285 ing dendritic processing, (2) simplified synaptic kinetics without vesicle depletion, (3) absence of286 network connectivity and population dynamics, and (4) deterministic framework excluding synap-287 tic noise. These limitations were chosen to maintain computational tractability while preserving288 essential mechanisms relevant to NMDA receptor kinetics and neuronal excitability.289 2.11 Reproducibility Statement290 All simulation code and analysis scripts are available athttps://github.com/borjkhani/Bifurcation_291 NMDA. Computational requirements include Python 3.8+ with specified dependencies and approx-292 10 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint imately 32 GB RAM for full parameter space exploration. Random seed handling ensures repro-293 ducible results, and detailed parameter files enable exact replication of all findings. Raw data and294 processed results are available upon reasonable request in accordance with institutional data sharing295 policies.296 3 Results297 3.1 Model Validation and Basic Neuronal Response298 The computational model reproduced characteristic pyramidal neuron dynamics under controlled299 stimulation conditions (Figure 3). Glutamatergic inputs (1 µM pulses) and continuous GABAergic300

activity (0.5 µM) generated distinct synaptic current profiles. NMDA currents exhibited301 slow kinetics with sustained activation, AMPA currents showed rapid transient responses, and302 GABA currents provided inhibitory modulation. Regular action potential firing occurred at 30.0 Hz303 with realistic membrane potential dynamics ranging from -75 mV to +50 mV. Intracellular calcium304 concentration ([Ca2+]i) oscillated between baseline and 0.858µM peaks (mean: 0.256 µM), reflecting305 NMDA receptor-mediated calcium influx. CaMKII phosphorylation levels at βNMDA = 0 .0520306 ms−1 demonstrated three distinct plasticity regimes: Long-Term Depression (LTD), metaplasticity307 transition zone, and Long-Term Potentiation (LTP) regions, with phosphorylation levels plotted on308 logarithmic scale over time.309 3.2 Information-Theoretic Analysis Reveals Optimal NMDA Receptor Modu-310 lation311 Information-theoretic analysis identified optimal NMDA receptor kinetics for neural coding (Figure312 4). Mutual information between neural responses and stimuli peaked at βNMDA = 0.028 ms−1 with313 maximum information transfer of 0.275 bits. Mutual information exhibited frequency-dependent314 characteristics, with highest values in the low-frequency range (0-30 Hz) and rapid decay at higher315 stimulation frequencies above 50 Hz. Neural response entropy increased with NMDA modulation316 strength, reaching a plateau atβNMDA = 0.383 ms−1 with peak entropy of 1.81 bits. Entropy demon-317 strated frequency-dependent modulation with a prominent peak at 185 Hz (2.89 bits), followed by318 sharp decline at higher frequencies. Error bars represent standard deviation across multiple trials.319 3.3 Bifurcation Analysis Reveals Period-Doubling Routes to Chaos320 Detailed bifurcation analysis in the low-frequency regime revealed systematic transitions in firing321 dynamics (Figure 5). Entropy and maximum Lyapunov exponent heatmaps identified chaotic re-322 gions concentrated in low-frequency, low- βNMDA parameter space. Phase portraits demonstrated323 progressive evolution from regular periodic firing ( βNMDA = 0.005 ms −1) through period-doubling324 cascades to chaotic dynamics ( βNMDA = 0.08 ms−1). Bifurcation diagrams showed period-doubling325 routes to chaos with pink regions indicating chaotic parameter ranges. ISI probability density func-326 tions revealed frequency band evolution from gamma (30-100 Hz) through beta (13-30 Hz) to alpha327 (8-13 Hz) distributions. CaMKII phosphorylation analysis across different βNMDA values (0.007,328 0.042, 0.082 ms −1) demonstrated distinct plasticity regimes: LTP region (high phosphorylation),329 transition zone, and LTD region (low phosphorylation).330 11 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 3.4 Frequency-Dependent Neural Dynamics and Phase Space Evolution331 Voltage traces and phase diagrams demonstrated systematic changes in neural dynamics across332 stimulation frequencies (Figure 6). At 2 Hz stimulation, neurons exhibited complex firing patterns333 with multiple βNMDA values producing distinct voltage trajectories and elaborate phase space struc-334 tures. At 5 Hz, moderate frequency stimulation showed earlier onset of irregular dynamics with335 simplified phase portraits. Higher stimulation frequencies produced progressive stabilization: 15336 Hz demonstrated rapid convergence to regular firing patterns, while 50 Hz stimulation resulted in337 highly regular dynamics with compressed phase space trajectories. Phase diagrams revealed sys-338 tematic evolution from complex multi-loop attractors at low frequencies to simple limit cycles at339 high frequencies. Voltage amplitudes ranged from -75 mV to +50 mV across all conditions, with340 firing patterns becoming increasingly predictable as stimulation frequency increased.341 3.5 Frequency-Dependent Chaos Threshold Erosion342 Bifurcation diagrams revealed systematic erosion of chaos thresholds with increasing stimulation343 frequency (Figure 7). At 2 Hz stimulation, chaotic regions (pink shading) occupied 18 parameter344 ranges (2.0% of βNMDA space), with complex bifurcation structures and ISI values ranging from345 0-500 ms. At 5 Hz, chaotic regions decreased to 22 ranges (2.4% coverage) with ISI compression to346 0-200 ms. Further frequency increases produced progressive stabilization: 10 Hz exhibited 25 chaotic347 regions (2.8% coverage) with ISI range 0-80 ms, while 15 Hz showed 20 regions (2.2% coverage) and348 ISI range 0-60 ms. At 50 Hz stimulation, chaos was nearly eliminated with only 5 regions (0.6%349 coverage) and tight ISI clustering around 15-18 ms. Bifurcation patterns evolved from complex350 multi-branch structures at low frequencies to simple periodic solutions at high frequencies.351 3.6 Oscillatory Band Evolution and Spectral Consolidation352 Frequency band analysis revealed systematic spectral evolution across stimulation rates (Figure 8).353 At 2 Hz stimulation, ISI distributions showed broad multi-band characteristics spanning gamma354 (30-100 Hz, blue), beta (13-30 Hz, red), alpha (8-13 Hz, green), theta (4-8 Hz, purple), and delta355 (0.5-4 Hz, yellow) frequency ranges. Empirical distributions demonstrated peak densities of 0.08 for356 beta band and 0.05 for alpha band. At 5 Hz stimulation, spectral content consolidated with reduced357 delta component and enhanced gamma representation. Progressive frequency increases produced358 systematic band elimination: 10 Hz stimulation showed dominant alpha band concentration (density359 = 1.0) with minimal beta and theta contributions. At 15 Hz, beta band dominance emerged (density360 = 0.5) with compressed alpha representation. At 50 Hz stimulation, complete gamma band con-361 centration occurred (density = 3.5) with elimination of all slower frequency components. Gaussian362 mixture model fits confirmed progressive spectral narrowing from multi-component distributions to363 single-component gamma-range concentration.364 3.7 GABAergic Inhibition Provides Frequency-Selective Stabilization365

GABAergic inhibition systematically modulated neural bifurcation dynamics across366 inhibition frequencies from 0-50 Hz (Figure 9). Control conditions (no GABA) exhibited extensive367 chaotic regions (pink shading) with complex bifurcation structures spanning ISI ranges from 0-100368 ms. GABA inhibition at 2 Hz produced minimal stabilization effects, maintaining similar chaotic369 parameter coverage. Progressive GABA frequency increases demonstrated systematic stabilization:370 5 Hz inhibition reduced chaotic regions and simplified bifurcation patterns, while 10 Hz further371 compressed chaotic parameter space. At 15 Hz and 20 Hz GABA inhibition, chaotic regions were372 12 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint substantially reduced with ISI ranges constrained to 20-80 ms. Complete chaos elimination occurred373 at 50 Hz GABA inhibition, producing stable dynamics with ISI clustering around 15-20 ms across the374 entire βNMDA parameter range. Bifurcation structures evolved from complex multi-branch patterns375 to simple periodic solutions with increasing GABA frequency.376 3.8 GABA Modulates CaMKII-Mediated Plasticity States377 CaMKII phosphorylation analysis revealed systematic GABA-dependent modulation of synaptic378 plasticity mechanisms (Figure 10). Aggregate CaMKII dynamics across all βNMDA values showed379 progressive suppression with increasing GABA frequencies: control conditions (0 Hz) reached maxi-380 mum phosphorylation levels of 2.5 ×10−23 M, while 50 Hz GABA reduced peak levels to 1.2 ×10−23381 M. Individual trajectory analysis at βNMDA = 0.007 ms−1 demonstrated GABA-dependent phospho-382 rylation suppression over 6-second time courses. Plasticity state transitions versus GABA frequency383 showed systematic shifts: βNMDA = 0.007 ms −1 decreased from 2.1 to 1.2 ×10−23 M, while higher384 βNMDA values maintained stable low phosphorylation levels. Phase diagrams revealed exponential385 decay relationships between CaMKII levels and βNMDA across GABA conditions. Parameter space386 analysis quantified plasticity region redistribution: 0 Hz GABA produced 63% LTD, 27% transition,387 and 10% LTP regions, while 50 Hz GABA shifted to 83% LTD, 17% transition, and minimal LTP388 coverage.389 4 Discussion390 Our computational analysis reveals that NMDA receptor kinetics fundamentally control neuronal391 dynamics through dual pathways, with broad implications across multiple neuropsychiatric con-392 ditions Hansen et al. (2021); Paoletti et al. (2023). While these findings have potential applica-393 tions to schizophrenia, autism spectrum disorders, Alzheimer’s disease, and chronic pain syndromes394 Gulchina et al. (2024); Zhou and Sheng (2023); Bruining et al. (2024), we focus our detailed dis-395 cussion on two specific domains where NMDA dysfunction plays particularly well-characterized396 roles: addiction-related memory formation and visual processing disorders. These applications397 demonstrate the translational potential of our quantitative framework for understanding cortical398 excitability and developing targeted therapeutic interventions.399 4.1 Dual Pathways Framework400 Two mechanistically distinct routes to firing irregularity emerged from our analysis of 2,942,093 ISI401 observations. High-frequency chaos (Pathway 1) occurs under rapid NMDA deactivation (βNMDA >402 0.06 ms−1) with strong synaptic drive, producing deterministic chaos with compromised information403 encoding (MI = 0.1847 bits vs. 0.2753 bits optimal) Durstewitz and Gabriel (2007); Toyoizumi and404 Abbott (2011). Prolonged activation irregularity (Pathway 2) results from slow NMDA deactivation405 (βNMDA < 0.02 ms −1) creating instability even under weak drive, with sustained calcium influx406 driving aberrant CaMKII phosphorylation Zhabotinsky (2000); Abraham (2008).407 The identification of an optimal kinetic window ( βNMDA = 0.028 ms −1; MI = 0.2753 bits)408 represents a critical balance point that maximizes spike timing information capacity while avoiding409 pathological states de Ruyter van Steveninck et al. (1997); Schreiber et al. (2009). This framework410 challenges traditional views attributing irregular firing solely to synaptic noise or network imbalance,411 instead revealing NMDA kinetics as master regulators of cortical excitabilityWang (1999); Ruggiero412 et al. (2024).413 13 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 4.2 model limitations and cience414 4.2.1 Pathological Memory Formation415 The slow NMDA deactivation pathway (Pathway 2) directly parallels kinetic alterations observed416 following chronic drug exposure Kalivas(2009); Wolf (2016); Volkow and Boyle(2023). Our findings417 demonstrate that prolonged receptor activation maintains elevated CaMKII phosphorylation (8.7 ±418 0.3 × 10−21 M vs. 1.8 ± 0.1 × 10−23 M for normal kinetics), creating conditions for pathological419 LTP that differs qualitatively from normal learning-related plasticity L¨ uscher and Malenka(2011);420 Pascoli et al. (2014).421 This prolonged activation enables formation of abnormally persistent drug-associated memories422 through sustained calcium influx and aberrant plasticity mechanisms Kauer and Malenka (2007);423 Hearing et al. (2022). Unlike normal memory formation requiring precisely timed calcium tran-424 sients, drug-induced memories exploit aberrantly extended NMDA activation to create difficult-to-425 reverse synaptic modifications Borjkhani et al. (2018a,b). The entropy characteristics in this regime426 suggest this pathway not only creates pathological plasticity but also disrupts normal information427 processing, potentially explaining cognitive inflexibility observed in addiction Goldstein and Volkow428 (2011). These findings complement our previous work showing that opioids can induce pathological429 theta oscillations associated with addiction memory formation (Borjkhani et al., 2018c), and extend430 our understanding of how different drugs of abuse alter neural computation through distinct ionic431 mechanisms (Borjkhani et al., 2022).432 4.2.2 Therapeutic Targeting Strategies433 Our findings suggest novel therapeutic approaches targeting NMDA kinetics during memory re-434 consolidation Nader et al. (2000); Lee et al. (2006). The chaotic dynamics in Pathway 1 indicate435 that pharmacologically accelerating receptor deactivation during memory retrieval could disrupt436 reconsolidation by degrading the neural code required for memory restabilization Lee et al. (2017).437 This approach could selectively target drug memories while preserving normal memory function.438 The frequency-dependent stability effects have important implications for cue-induced relapse.439 The systematic threshold erosion with increasing frequency (72440 4.3 Applications to Visual Processing Disorders441 4.3.1 Retinal Pathophysiology442 NMDA receptors in retinal ganglion cells are critical for contrast sensitivity, direction selectivity,443 and light adaptation Manookin et al. (2010); Chen et al. (2016). Our dual-pathway framework444 reveals mechanistically distinct routes to retinal dysfunction. The prolonged activation pathway445 maintains sustained calcium influx directly relevant to excitotoxic mechanisms in glaucoma, where446 chronic glutamate elevation leads to retinal ganglion cell death Seki and Lipton (2008); Boccuni447 and Fairless (2022). The quantitative relationship between NMDA kinetics and calcium homeostasis448 provides specific targets for neuroprotective interventions Bezprozvanny (2009).449 The high-frequency chaos pathway may explain acute retinal injury responses in diabetic retinopa-450 thy, where rapid metabolic changes alter NMDA kinetics and disrupt normal information encoding451 Bai et al. (2013); Hartwick et al. (2008). The degraded mutual information observed in this regime452 could underlie visual processing deficits during acute hyperglycemic episodes.453 14 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 4.3.2 Cortical Visual Processing454 The systematic oscillatory pattern shifts have direct relevance for cortical visual processing, where455 gamma oscillations mediate feature binding and attention while alpha rhythms control spatial atten-456 tion and predictive coding Jensen and Mazaheri (2010); Singer (1999). Our frequency-dependent457 analysis reveals that NMDA kinetics fundamentally control the balance between these computa-458 tional modes Fox and Daw (1992); Nowak et al. (1997).459 Visual processing disorders may result from NMDA kinetic alterations disrupting normal oscil-460 latory balance, potentially explaining visual attention deficits in conditions like amblyopia where461 NMDA function changes during critical developmental periods Hensch (2005); Takesian and Hensch462 (2022); Fagiolini et al. (2024). The optimal kinetic window we identify may represent evolutionary463 optimization for experience-dependent visual development Bavelier et al. (2010); Meredith et al.464 (2023).465 4.4 GABAergic Modulation and Circuit Stabilization466 GABAergic inhibition provided frequency-selective stabilization, expanding stable parameter space467 by 34.2468 For addiction treatment, GABAergic modulation could prevent transition to chaotic regimes469 during cue exposure while maintaining normal memory encoding capacity. In visual disorders,470 frequency-selective GABA enhancement could restore optimal oscillatory balance required for visual471 attention and processing Whittington et al. (2000); Brunel and Hakim (1999). The complete chaos472 elimination at 50 Hz GABA demonstrates the therapeutic potential of precisely timed inhibitory473 modulation Yizhar et al. (2011).474 4.5 Clinical Translation and Precision Medicine475 The parameter-dependent effects we identify suggest that therapeutic interventions should be tai-476 lored to individual NMDA dysfunction patterns rather than employing broad-spectrum approaches477 Glasgow et al. (2022); Traynelis et al. (2010). For patients showing evidence of slow NMDA kinet-478 ics (Pathway 2), interventions that accelerate receptor deactivation during memory retrieval may479 be beneficial for addiction treatment. Conversely, individuals with rapid kinetics and high neural480 variability may require stabilization approaches enhancing GABAergic inhibition.481 Our computational framework suggests several neurophysiological biomarkers for assessing cir-482 cuit states and guiding personalized interventions: EEG-derived entropy measures could indicate483 proximity to chaotic regimes Ellner and Turchin (1995); Wolf et al. (1985), gamma/beta power484 ratios could reflect underlying NMDA kinetic states Uhlhaas and Singer (2010); Donner and Siegel485 (2011), and stimulus-response mutual information could quantify encoding process integrity and486 treatment efficacy Goebel et al. (2005); Reeke and Coop (2004).487 Rather than broad NMDA antagonism that can impair normal cognitive function, our find-488 ings suggest kinetically-specific approaches Javitt (2007); Lisman et al. (2008). Positive allosteric489 modulators that normalize deactivation rates could restore optimal information processing while490 preserving beneficial NMDA-dependent functions Lutzu and Castillo (2021); Carles et al. (2024).491 The frequency-selective effects of GABAergic modulation indicate that targeted stimulation proto-492 cols could provide therapeutic benefits for disorders involving NMDA dysfunction.493 15 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 4.6 Model Limitations and Future Directions494 Several limitations should be acknowledged when interpreting our findings. Our single-cell approach495 cannot capture network-level phenomena like synchronization and large-scale oscillations crucial for496 addiction circuits and visual processing networks Cabral et al. (2014); Anticevic et al. (2012).497 NMDA receptor subtypes and kinetic properties vary across brain regions, requiring region-specific498 parameter adjustments for clinical applications Monyer et al. (1992); Standaert et al. (1999); Sheng499 et al. (1994). Different neuronal subtypes exhibit distinct NMDA-dependent behaviors that our500 generalized model does not capture Spruston (2008); Freund and Buzs´ aki(1996).501 Despite these limitations, the quantitative relationships we establish between receptor kinetics502 and neural dynamics provide a foundational framework for understanding NMDA-related pathology.503 Future experimental validation should include dynamic clamp experiments manipulating NMDA504 kinetics directly Harsch and Robinson (2000); Vargas-Caballero and Robinson (2004), optogenetic505 approaches for selective in vivo modification Boyden (2011), and high-density electrophysiology506 measuring oscillatory changes in behaving animals during addiction-related and visual processing507 tasks.508 Network-level extensions should incorporate recurrent connectivity patterns Destexhe and Se-509 jnowski (2009); Izhikevich (2006), multiple cell types with distinct NMDA properties, and region-510 specific circuit architectures relevant to addiction and visual processing Deco et al. (2008, 2023).511 These developments will advance understanding of NMDA receptors as master regulators of corti-512 cal computation and therapeutic targets for diverse brain disorders, with particular relevance for513 developing precision medicine approaches to addiction treatment and visual processing disorder514 interventions.515 5 Conclusion516 Our computational investigation reveals NMDA receptor kinetics as fundamental controllers of neu-517 ronal excitability and synaptic plasticity through dual mechanistic pathways. Analysis of 2,942,093518 inter-spike intervals identified two distinct routes to firing irregularity: high-frequency chaos under519 rapid deactivation and prolonged activation irregularity under slow deactivation, with an optimal520 kinetic window at βNMDA = 0.028 ms−1 maximizing information encoding.521 These findings provide mechanistic insights into addiction-related memory formation, where522 prolonged NMDA activation creates conditions for pathological plasticity, and visual processing523 disorders, where altered kinetics disrupt retinal function and cortical oscillatory balance. GABAer-524 gic inhibition offers frequency-selective stabilization, expanding stable parameter space by 34.2%525 while preserving beneficial gamma rhythms.526 The quantitative relationships between molecular receptor properties and network dynamics527 establish a framework for precision medicine approaches targeting kinetically-specific interventions.528 As tools for measuring and manipulating NMDA function advance, these insights will prove crucial529 for translating molecular discoveries into effective clinical interventions across NMDA-related brain530 disorders.531 6 Data and Code Availability532 All simulation code, analysis scripts, and datasets are publicly available at: https://github.com/533 borjkhani/Bifurcation_NMDA. The repository includes fully documented simulation code, param-534 eter files, analysis scripts, raw and processed data files, figure generation scripts, and computational535 16 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint environment setup instructions. Simulations were performed using Python 3.8 with fixed random536 seeds (seed = 42) for complete reproducibility.537 Acknowledgments538 We thank Prof. Maciej Wojtkowski for helpful discussions and support. 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It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint A Statistical Analysis Methods804 A.1 Dataset Characteristics805 The simulation generated 2,942,093 ISI observations across 1,961 parameter combinations. Quality806 control procedures included ISI filtering (2-2000 ms), outlier detection, and convergence verification.807 A.2 Core Statistical Procedures808 Two-way ANOVA examined main effects of βN M DA categories and stimulation frequency on neu-809 ronal dynamics, with post-hoc comparisons using independent samples t-tests and Cohen’s d effect810 sizes.811 A.3 Dynamical Analysis Methods812 Shannon entropy: H = − P20 k=1 pk log2 pk Maximum Lyapunov exponents: Wolf et al. algo-813 rithm with embedding dimension d=5, time delay τ=5 ms Mutual information: M I(X; Y ) =814 P x,y p(x, y) log2 p(x,y) p(x)p(y)815 A.4 Software and Reproducibility816 Analyses used Python 3.8 with NumPy 1.21.0, SciPy 1.7.0, scikit-learn 1.0.0. Code available with817 fixed random seeds (seed=42) for reproducibility.818 24 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint Model Development & Parameter Space Dynamical Analysis Methods Key Findings: Dual Pathways F ramework Clinical T ranslation & Applications Hodgkin–Huxley Pyramidal Neuron • Na+, K +, Ca2+ currents • NMDA, AMP A, GABA • CaMKII phos- phorylation βNMDA 0.01–0.1 ms−1 20 log values Stimulation Freq 1–250 Hz 25 values Computational Simulation • Runge–Kutta 4th • ∆t = 0.05 ms • 1 961 combos • 2 942 093 ISI Shannon Entropy H = − ∑pk log2pk Maximum Lyapunov Exp. Chaos detection Mutual Information Info encoding Bifurcation Analysis Period-doubling Frequency Band Analysis γ,β,α,θ,δ Statistical Analysis Two-way ANOVA p 0.06 ms−1 Entropy: 1.441 bits Compromised encoding Pathway 2: Prolonged Activation βNMDA< 0.02 ms−1 Entropy: 1.347 bits Sustained Ca2+ Optimal Window βNMDA= 0.028 MI = 0.2753 bits Max information GABA Effects 34.2% ex- pansion 43% chaos reduction Frequency-selective Addiction Memory Interventions • Pathological L TP • Reconsolidation • Kinetic targets Visual Pro- cessing Disorders • Retinal dysfunction • Oscilla- tion restore • γ/αbalance Therapeutic Strategies • Precision medicine • Kinetic modulators • Biomarkers Parameter DefinitionAnalysis PipelineMechanistic Insights Data GenerationPattern RecognitionClinical Translation Methodology Flow: Direct Cross Scale of Analysis: • 1 961 combinations • 2 942 093 ISI obs. • 20βNMDAvalues • 25 frequencies • 10-s runs • Replicates Figure 1: Comprehensive computational workflow for investigating NMDA receptor ki- netics and neuronal dynamics. The study employed a systematic four-stage approach: (1) Model Development & Parameter Space - Implementation of a detailed Hodgkin-Huxley pyramidal neuron model with systematic exploration of NMDA receptor closing rates (βN M DA: 0.01-0.1 ms −1, 20 values) and glutamatergic stimulation frequencies (1-250 Hz, 25 values). GABAergic modulation was tested at three levels (0, 25, 50 Hz), generating 1,500 parameter combinations (500 base × 3 GABA conditions). (2) Dynamical Analysis Methods - Application of multiple complementary techniques including Shannon entropy analysis, maximum Lyapunov exponent calculation, mutual information quantification, bifurcation analysis, frequency band decomposition, and statistical vali- dation. (3) Key Findings: Dual Pathways Framework - Identification of two distinct routes to firing irregularity (Pathway 1: high-frequency chaos; Pathway 2: prolonged activation) and an optimal kinetic window for information encoding, alongside GABAergic modulation effects. (4) Clinical Translation & Applications - Direct relevance to addiction memory interventions, visual processing disorders, and therapeutic strategy development. The analysis encompassed 2,942,093 inter-spike interval observations across multiple computational replicates. Solid arrows indicate direct analyti- cal flow; dotted arrows represent cross-validation and mechanistic connections between findings and applications. 25 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 𝑰 𝑵𝒂 𝑰 𝑪 𝑰𝑵𝒂𝑷 𝑰𝑲𝒅𝒓 𝑰 𝑨 𝑰 𝑴 𝑰𝑪𝒂 𝑰 𝒔𝑨𝑯𝑷 𝑰𝑵𝑴𝑫𝑨 𝑰𝑨𝑴𝑷𝑨 𝑰𝑮𝑨𝑩𝑨 𝑰𝑮𝑨𝑩𝑨 𝑮𝑨𝑩𝑨 𝑮𝒍𝒖𝒕𝒂𝒎𝒂𝒕𝒆 Ca2+ K+ Na+ Figure 2: Synaptic inputs and ionic currents in the modeled neuron. This schematic illustrates the synaptic and intrinsic ionic currents included in the model. The total synaptic current consists of AMPA, NMDA, and GABAergic components, where AMPA and NMDA mediate excitatory transmission, with NMDA exhibiting a voltage-dependent Mg2+ block, while GABAergic currents provide inhibition. The intrinsic ionic currents include fast and persistent sodium ( INa, INaP), various potassium currents regulating repolarization and adaptation ( IKdr, IA, IM), calcium- mediated currents ( ICa, IC), and slow afterhyperpolarization and leak currents ( IsAHP, IL). These currents collectively shape neuronal excitability, synaptic integration, and firing dynamics. 26 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 0.0 0.5 1.0 Glutamate Input (?M) Glutamatergic Synaptic Input 0.0 0.5 1.0 GABA (?M) GABAergic Input ?30 ?20 ?10 0 INMDA (nA) NMDA Current ?20 ?10 0 IAMPA (nA) AMPA Current 0 20 40 IGABA (nA) GABA Current ?50 0 50 Membrane Potential (mV) Spike Rate: 30.0 Hz Action Potentials and Neural Activity 0.00 0.25 0.50 0.75 /uni0000003e/uni00000026/uni00000044/uni000000f0/uni00000040i (?M) Mean: 0.256 ?M Peak: 0.858 ?M Intracellular Calcium Dynamics 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 Time (s) /uni00000014/uni00000013/uni00000015/uni00000016 /uni00000014/uni00000013/uni00000015/uni00000015 /uni00000014/uni00000013/uni00000015/uni00000014 /uni00000014/uni00000013/uni00000015/uni00000013 Phosphorylated CaMKII (?M, log scale) Long-Term Depression Metaplasticity Transition Long-Term Potentiation 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 CaMKII Phosphorylation LTD Region Transition LTP Region Neural Dynamics and Synaptic Plasticity: CaMKII-Mediated Learning A B C D E Figure 3: Neural dynamics and synaptic plasticity: CaMKII-mediated learning. (A) Synaptic input patterns: glutamatergic stimulation (left, 1 µM pulses) and GABAergic inhibitory input (right, continuous background activity). (B) Synaptic currents showing NMDA-mediated (INMDA), AMPA-mediated (I AMPA), and GABA-mediated ( IGABA) responses during stimulation. (C) Action potential generation and neural activity with spike rate of 30.0 Hz, demonstrating realistic membrane potential dynamics. (D) Intracellular calcium dynamics ([Ca 2+]i) with mean concentration of 0.256 µM and peak values reaching 0.858 µM, reflecting NMDA receptor-mediated calcium influx. (E) CaMKII phosphorylation dynamics ( βNMDA = 0.0520) showing distinct plastic- ity regimes: Long-Term Depression (LTD) region, metaplasticity transition zone, and Long-Term Potentiation (LTP) region, with CaMKII phosphorylation levels plotted on logarithmic scale over time. 27 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 0.0 0.2 0.4 0.6 0.8 NMDA 0.235 0.240 0.245 0.250 0.255 0.260 0.265 0.270 0.275Mutual Information (bits) Peak: 0.028 0.275 bits /uni00000024/uni0000000c/uni00000003/uni00000030/uni00000058/uni00000057/uni00000058/uni00000044/uni0000004f/uni00000003/uni0000002c/uni00000051/uni00000049/uni00000052/uni00000055/uni00000050/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni00000059/uni00000056/uni00000003NMDA 0 50 100 150 200 Stimulation Frequency (Hz) 0.0 0.1 0.2 0.3 0.4 0.5 0.6Mutual Information (bits) B) Mutual Information vs Frequency High MI region 0.0 0.2 0.4 0.6 0.8 NMDA 0.5 1.0 1.5 2.0 2.5Entropy (bits) Peak: ?=0.383 1.81 bits /uni00000026/uni0000000c/uni00000003/uni00000028/uni00000051/uni00000057/uni00000055/uni00000052/uni00000053/uni0000005c/uni00000003/uni00000059/uni00000056/uni00000003NMDA 0 50 100 150 200 Stimulation Frequency (Hz) 0.0 0.5 1.0 1.5 2.0 2.5 3.0Entropy (bits) Peak: 185 Hz 2.89 bits D) Entropy vs Stimulation Frequency Figure 4: Information-theoretic analysis reveals optimal NMDA receptor modulation and frequency-dependent neural coding. (A) Mutual information between neural responses and stimuli as a function of NMDA receptor modulation strength (β NMDA). Peak information transfer occurs at βNMDA = 0.028, corresponding to 0.275 bits. (B) Mutual information varies with stimulation frequency, showing maximal information content in the low-frequency range (0-30 Hz, shaded region) with rapid decay at higher frequencies. (C) Neural response entropy increases with NMDA modulation strength, reaching a plateau around βNMDA = 0.4 (peak: 1.81 bits at βNMDA = 0.383). Error bars represent standard deviation across trials. (D) Entropy exhibits frequency- dependent modulation with a prominent peak at 185 Hz (2.89 bits), followed by a sharp decline. Error bars represent standard deviation. The analysis demonstrates that moderate NMDA receptor modulation optimizes information transfer while maintaining response diversity, with distinct coding regimes for low-frequency information transmission and high-frequency response entropy. 28 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint A B C D E F Figure 5: Bifurcation analysis and oscillatory dynamics. (A-B) Entropy and MLE heatmaps for low-frequency, low-βNMDA parameter space. (C) Phase portraits showing transition from regular to chaotic firing. (D) Bifurcation diagram revealing period-doubling route to chaos (red regions indicate chaotic dynamics). (E) ISI probability density functions categorized by frequency bands. (F) CaMKII phosphorylation levels across plasticity regimes: LTP (orange), transition (green), LTD (blue). 29 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint A B C D Figure 6: Neural dynamics across stimulation frequencies. Voltage traces and phase diagrams showing progressive destabilization from (A) 2 Hz stable dynamics with complex bifurcations, (B) 5 Hz moderate frequency showing earlier chaos onset, (C) 15 Hz rapid destabilization, to (D) 50 Hz immediate chaotic dynamics with highly irregular patterns. 30 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001b /uni00000013 /uni00000014/uni00000013/uni00000013 /uni00000015/uni00000013/uni00000013 /uni00000016/uni00000013/uni00000013 /uni00000017/uni00000013/uni00000013 /uni00000018/uni00000013/uni00000013/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000024 /uni00000015/uni00000003/uni0000002b/uni0000005d/uni00000003/uni00000036/uni00000057/uni0000004c/uni00000050/uni00000058/uni0000004f/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni0000000b/uni00000003/uni00000020/uni00000003/uni00000013/uni00000011/uni00000016/uni0000001b/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001b /uni00000013 /uni00000018/uni00000013 /uni00000014/uni00000013/uni00000013 /uni00000014/uni00000018/uni00000013 /uni00000015/uni00000013/uni00000013/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000025 /uni00000018/uni00000003/uni0000002b/uni0000005d/uni00000003/uni00000036/uni00000057/uni0000004c/uni00000050/uni00000058/uni0000004f/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni0000000b/uni00000003/uni00000020/uni00000003/uni00000013/uni00000011/uni00000016/uni0000001b/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001b /uni00000013 /uni00000015/uni00000013 /uni00000017/uni00000013 /uni00000019/uni00000013 /uni0000001b/uni00000013/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000026 /uni00000014/uni00000013/uni00000003/uni0000002b/uni0000005d/uni00000003/uni00000036/uni00000057/uni0000004c/uni00000050/uni00000058/uni0000004f/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni0000000b/uni00000003/uni00000020/uni00000003/uni00000013/uni00000011/uni00000016/uni0000001b/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001b /uni00000013 /uni00000014/uni00000013 /uni00000015/uni00000013 /uni00000016/uni00000013 /uni00000017/uni00000013 /uni00000018/uni00000013 /uni00000019/uni00000013/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000027 /uni00000014/uni00000018/uni00000003/uni0000002b/uni0000005d/uni00000003/uni00000036/uni00000057/uni0000004c/uni00000050/uni00000058/uni0000004f/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni0000000b/uni00000003/uni00000020/uni00000003/uni00000013/uni00000011/uni00000016/uni0000001b/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001b NMDA /uni00000015/uni00000011/uni00000018 /uni00000018/uni00000011/uni00000013 /uni0000001a/uni00000011/uni00000018 /uni00000014/uni00000013/uni00000011/uni00000013 /uni00000014/uni00000015/uni00000011/uni00000018 /uni00000014/uni00000018/uni00000011/uni00000013 /uni00000014/uni0000001a/uni00000011/uni00000018/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000028 /uni00000018/uni00000013/uni00000003/uni0000002b/uni0000005d/uni00000003/uni00000036/uni00000057/uni0000004c/uni00000050/uni00000058/uni0000004f/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni0000000b/uni00000003/uni00000020/uni00000003/uni00000013/uni00000011/uni00000016/uni0000001b/uni0000000c Figure 7: Frequency-dependent bifurcation landscapes and chaos onset thresholds. (A- E) Bifurcation diagrams showing inter-spike interval distributions versus βNMDA across stimulation frequencies from 2 Hz to 50 Hz. Pink shading indicates chaotic regions. Progressive frequency increases demonstrate systematic erosion of stability thresholds: (A) 2 Hz exhibits complex bifur- cations with chaos onset at βNMDA ≈ 0.012 ms −1, (B) 5 Hz shows earlier destabilization, (C) 10 Hz displays limited chaotic windows, (D) 15 Hz demonstrates compressed parameter ranges, and (E) 50 Hz maintains remarkable stability with tight gamma-frequency ISI clustering (15-18 ms) and minimal chaotic behavior. 31 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint /uni00000013/uni00000014/uni00000013/uni00000013/uni00000015/uni00000013/uni00000013/uni00000016/uni00000013/uni00000013/uni00000017/uni00000013/uni00000013/uni00000018/uni00000013/uni00000013 /uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013 /uni00000013/uni00000011/uni00000013/uni00000014 /uni00000013/uni00000011/uni00000013/uni00000015 /uni00000013/uni00000011/uni00000013/uni00000016 /uni00000013/uni00000011/uni00000013/uni00000017 /uni00000013/uni00000011/uni00000013/uni00000018 /uni00000013/uni00000011/uni00000013/uni00000019 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/uni00000013/uni00000014/uni00000013/uni00000015/uni00000013/uni00000016/uni00000013/uni00000017/uni00000013 /uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000013/uni00000011/uni00000013/uni00000013 /uni00000013/uni00000011/uni00000013/uni00000015 /uni00000013/uni00000011/uni00000013/uni00000017 /uni00000013/uni00000011/uni00000013/uni00000019 /uni00000013/uni00000011/uni00000013/uni0000001b /uni00000013/uni00000011/uni00000014/uni00000013 /uni0000002a/uni00000044/uni00000058/uni00000056/uni00000056/uni0000004c/uni00000044/uni00000051/uni00000003/uni00000029/uni0000004c/uni00000057/uni00000056 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 /uni00000028/uni00000050/uni00000053/uni0000004c/uni00000055/uni0000004c/uni00000046/uni00000044/uni0000004f /uni00000027/uni0000004c/uni00000056/uni00000057/uni00000055/uni0000004c/uni00000045/uni00000058/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000056 /uni0000002a/uni00000044/uni00000058/uni00000056/uni00000056/uni0000004c/uni00000044/uni00000051 /uni00000029/uni0000004c/uni00000057/uni00000056 Figure 8: Frequency band analysis of neural oscillations across stimulation rates. (A-E) Top panels show empirical probability density distributions of inter-spike intervals decomposed into physiological frequency bands: gamma (30-100 Hz, blue), beta (13-30 Hz, red), alpha (8-13 Hz, green), theta (4-8 Hz, purple), and delta (0.5-4 Hz, yellow) across stimulation frequencies from 2 Hz to 50 Hz. Bottom panels display corresponding Gaussian mixture model fits. Progressive stim- ulation rate increases produce systematic spectral consolidation: (A) 2 Hz shows broad multi-band distributions, (B-D) intermediate frequencies (5-15 Hz) exhibit gradual gamma-band dominance, and (E) 50 Hz stimulation results in tight gamma-range concentration with minimal spectral diver- sity. 32 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint /uni00000013/uni00000011/uni00000013/uni00000013/uni00000013/uni00000011/uni00000013/uni00000014/uni00000013/uni00000011/uni00000013/uni00000015/uni00000013/uni00000011/uni00000013/uni00000016/uni00000013/uni00000011/uni00000013/uni00000017/uni00000013/uni00000011/uni00000013/uni00000018/uni00000013/uni00000011/uni00000013/uni00000019/uni00000013/uni00000011/uni00000013/uni0000001a/uni00000013/uni00000011/uni00000013/uni0000001b/uni00000013/uni00000011/uni00000013/uni0000001c /uni00000013 /uni00000015/uni00000013 /uni00000017/uni00000013 /uni00000019/uni00000013 /uni0000001b/uni00000013 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/uni00000014/uni00000013/uni00000013/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000010/uni00000036/uni00000053/uni0000004c/uni0000004e/uni00000048/uni00000003/uni0000002c/uni00000051/uni00000057/uni00000048/uni00000055/uni00000059/uni00000044/uni0000004f/uni00000003/uni0000000b/uni00000050/uni00000056/uni0000000c /uni00000026/uni0000004b/uni00000044/uni00000052/uni00000057/uni0000004c/uni00000046/uni00000003/uni00000024/uni00000055/uni00000048/uni00000044 /uni00000018/uni00000013/uni00000003/uni0000002b/uni0000005d /uni0000002a /uni0000002a/uni00000024/uni00000025/uni00000024/uni00000003/uni0000002c/uni00000051/uni0000004b/uni0000004c/uni00000045/uni0000004c/uni00000057/uni0000004c/uni00000052/uni00000051/uni0000001d/uni00000003/uni00000018/uni00000013/uni00000003/uni0000002b/uni0000005d /uni0000002a/uni00000024/uni00000025/uni00000024/uni00000010/uni00000030/uni00000048/uni00000047/uni0000004c/uni00000044/uni00000057/uni00000048/uni00000047/uni00000003/uni00000031/uni00000048/uni00000058/uni00000055/uni00000044/uni0000004f/uni00000003/uni00000025/uni0000004c/uni00000049/uni00000058/uni00000055/uni00000046/uni00000044/uni00000057/uni0000004c/uni00000052/uni00000051/uni00000003/uni00000027/uni0000005c/uni00000051/uni00000044/uni00000050/uni0000004c/uni00000046/uni00000056 Figure 9: GABAergic inhibition modulates neural bifurcation dynamics and synaptic plasticity. (A-G) Bifurcation diagrams showing inter-spike interval patterns versus βNMDA under increasing GABA inhibition frequencies (0-50 Hz). Pink shading indicates chaotic regions. GABA progressively stabilizes dynamics, with 50 Hz completely eliminating chaos. (H) CaMKII phospho- rylation dynamics across GABA conditions, showing plasticity state transitions from LTP (green) through transition zones to LTD (pink) regions. GABA inhibition systematically reduces CaMKII levels and shifts plasticity thresholds, demonstrating frequency-dependent modulation of synaptic plasticity mechanisms. 33 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint 0 1 2 3 4 5 6 Time (s) 0.0 0.5 1.0 1.5 2.0 2.5Phospho-CaMKII ( M) 1e 23 A A. CaMKII Dynamics with Uncertainty (All NMDA Values) GABA 0 Hz GABA 20 Hz GABA 50 Hz 0 1 2 3 4 5 6 Time (s) 0.0 0.5 1.0 1.5 2.0 2.5Phospho-CaMKII ( M) 1e 23 B B. Individual Trajectories ( NMDA 0.007) GABA 0 Hz GABA 20 Hz GABA 50 Hz 0 10 20 30 40 50 GABA Frequency (Hz) 0.0 0.5 1.0 1.5 2.0 2.5Final CaMKII Level ( M) 1e 23 C C. Plasticity State Transitions vs GABA Frequency NMDA = 0.007 NMDA = 0.020 NMDA = 0.050 NMDA = 0.080 0.00 0.02 0.04 0.06 0.08 NMDA 0.0 0.5 1.0 1.5 2.0 2.5Final CaMKII Level ( M) 1e 23 D D. Plasticity Phase Diagram\nvs NMDA GABA 0 Hz GABA 2 Hz GABA 5 Hz GABA 10 Hz GABA 15 Hz GABA 20 Hz GABA 50 Hz 0.00 0.02 0.04 0.06 0.08 NMDA 0.0 0.5 1.0 1.5 2.0 2.5Final CaMKII 1e 23 E1 E1. GABA 0 Hz 0.00 0.02 0.04 0.06 0.08 NMDA 0.0 0.5 1.0 1.5 2.0 2.5Final CaMKII 1e 23 E2 E2. GABA 20 Hz 0.00 0.02 0.04 0.06 0.08 NMDA 0.0 0.5 1.0 1.5 2.0 2.5Final CaMKII 1e 23 E3 E3. GABA 50 Hz 0 Hz 20 Hz 50 Hz GABA Frequency 0 20 40 60 80 100 120 Parameter Space Coverage (%)63% 27% 10% 80% 17% 83% 17% 3 regions 3 regions 2 regions F F. Plasticity Region Distribution Across NMDA Parameter Space LTD Region Transition Region LTP Region GABA-Mediated Modulation of CaMKII Phosphorylation and Synaptic Plasticity Comprehensive Analysis of LTP/LTD State Transitions Figure 10: GABA-mediated modulation of CaMKII phosphorylation and synaptic plas- ticity. (A) CaMKII dynamics across all βNMDA values showing uncertainty bands for different GABA frequencies (0, 20, 50 Hz). (B) Individual CaMKII trajectories at βNMDA = 0.007 ms −1 demonstrating GABA-dependent suppression. (C) Plasticity state transitions versus GABA fre- quency for four βNMDA values, with horizontal dashed lines indicating LTP/LTD thresholds. (D) Phase diagram showing CaMKII levels versus βNMDA across GABA frequencies. (E1-E3) Detailed CaMKII curves for 0, 20, and 50 Hz GABA with plasticity region color coding. (F) Parameter space distribution showing progressive shift from LTP-dominant (63%) to LTD-dominant (83%) states with increasing GABA inhibition. 34 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted September 11, 2025. ; https://doi.org/10.1101/2025.09.06.674628doi: bioRxiv preprint