08.09.2026 In the brain, what matters is not only whether a signal reaches a nerve cell, but also how long its chemical gate remains open. A team led by Dr Mehdi Borjkhani from the International Centre for Translational Eye Research (ICTER) has demonstrated in a computational model that both excessively fast and excessively slow NMDA-receptor deactivation can disrupt neuronal activity. Importantly, these extremes in cessation rates lead to instability through two distinct mechanisms.
Every thought, image, and memory relies on electrical impulses transmitted by neurons. These impulses cannot be completely uniform, but neither can they be entirely unpredictable. The brain needs controlled variability: enough to encode new information, but not so much that the signal descends into chaos.
One of the regulators of this balance is the NMDA receptor. It can be compared to a gate with a built-in timer. After binding glutamate, it opens a pathway for ions, including calcium, and then gradually closes. Calcium activates processes responsible for synaptic plasticity-the ability of connections between neurons to become stronger or weaker. This plasticity is the biological basis of learning and memory. If the gate closes at the wrong rate, however, the neuron’s firing rhythm may break down.
The study, described in the article NMDA receptor kinetics drive distinct routes to chaotic firing in pyramidal neurons, was published in Frontiers in Computational Neuroscience. The first and corresponding author is Dr Mehdi Borjkhani from ICTER and the Institute of Physical Chemistry of the Polish Academy of Sciences. The research team also included Hadi Borjkhani, Morteza A. Sharif, Fariba Bahrami, and Mahyar Janahmadi, representing research institutions in Berlin, Urmia, and Tehran.
“Usually, we ask whether the NMDA receptor is functioning properly. Our results show that an equally important question is how quickly it stops working. The same receptor may support efficient information transmission or destabilize a neuron, depending on its closing time and the rhythm of incoming signals,” says Dr Mehdi Borjkhani, the lead author of the publication.
More than 2.9 million inter-spike intervals
The scientists used an advanced model of a pyramidal neuron, one of the main types of excitatory cells in the cerebral cortex. The model included sodium, potassium, and calcium channels, as well as three important types of synaptic receptors: the excitatory NMDA and AMPA receptors, and the inhibitory GABA receptor. The researchers also incorporated the CaMKII pathway. CaMKII is a calcium-dependent enzyme involved in consolidating changes in the connections between neurons.
Each simulation covered 10 seconds of neuronal activity. Calculations were performed with a time step of 0.05 milliseconds, and the first two seconds were discarded to remove the model’s transient response. Stimulation was delivered in pulses lasting 5 milliseconds. The researchers then systematically varied the stimulation frequency and the βNMDA parameter, which determines the receptor’s closing rate.
Within the most physiologically relevant range, βNMDA was varied from 0.002 to 0.1 ms⁻¹. This corresponded to receptor activation windows ranging from approximately 500 to 10 milliseconds. In total, the researchers analyzed more than 2.9 million intervals between consecutive spikes, known as inter-spike intervals.
The model reproduced the fundamental properties of real pyramidal neurons, including a resting potential of approximately -65 mV, a firing threshold close to -45 mV, and an action-potential amplitude of 80-100 mV. Compared with results obtained using the specialized NEURON simulator, the relative error remained below 0.1%.
Two routes to chaos
The analysis revealed two distinct scenarios in which the neuron lost its stable rhythm. The first emerged when the NMDA receptor deactivated relatively quickly while the neuron received signals at particular frequencies. The firing pattern then became chaotic, and the ability to encode information reliably declined. In this region of the parameter space, mutual information was approximately 0.185 bits, compared with around 0.275 bits at the optimum point.
This was not random noise. Positive Lyapunov exponents, entropy analysis, and bifurcation diagrams all pointed to deterministic chaos. This means that a very small change in the initial conditions could eventually produce a completely different firing pattern, even though the model contained no random source of interference.
The second route emerged when NMDA deactivation was very slow, with βNMDA falling below 0.02 ms⁻¹. The receptor remained active for a long time even under weak stimulation. This prolonged duration resulted in sustained calcium influx and subsequent CaMKII phosphorylation. In the model, it created conditions conducive to excessive, long-term strengthening of synapses.
“Chaos in this study does not mean ordinary disorder or random interference. It is a precisely identifiable dynamical state. Importantly, it can be reached through two routes: excessively short or excessively long NMDA-receptor activation. These mechanisms may require entirely different forms of intervention,” explains Dr Mehdi Borjkhani.
Between these two extremes, the scientists identified an optimal window. At a βNMDA value of 0.042 ms⁻¹, which approximately corresponds to a closing time of 24 milliseconds, mutual information reached 0.275 bits. According to the measure used in the model, this was the point at which the spike pattern could best distinguish between different input frequencies while maintaining stability.
Frequency can restore rhythm
Stimulation frequency proved to be another important regulator. At 2 Hz, the researchers identified as many as 18 separate parameter ranges that produced chaos. As the frequency increased, the chaotic regions became narrower and shifted towards increasingly slow NMDA deactivation. At 50 Hz, chaos was almost completely suppressed, while the intervals between spikes became concentrated within the 15-18 millisecond range, corresponding to gamma-band activity.
GABAergic inhibition, the nervous system’s natural “brake,” produced an even stronger effect. It expanded the stable parameter space by 34.2%, primarily limiting slower, irregular patterns while preserving fast gamma activity. With GABA stimulation at 50 Hz, chaos disappeared across the entire analyzed βNMDA range.
The modeled states of synaptic plasticity also changed. Without GABA stimulation, 65% of the parameter space was classified as long-term depression, 25% as a transitional state, and 10% as long-term potentiation. With GABA stimulation at 20 Hz, the share of the latter state fell to 3%. At 50 Hz, it disappeared entirely. The authors emphasize that this was a qualitative classification based on thresholds defined within the model, rather than a direct biological measurement.
Why is this important?
One potential application is a better understanding of addiction. Memories associated with psychoactive substances can be exceptionally persistent and may trigger cravings even after long periods of abstinence. The model’s results suggest that prolonged NMDA activation may sustain calcium influx and excessive CaMKII activity, promoting the consolidation of such pathological memories. In the future, a map linking receptor kinetics with stimulation frequency could support more precisely timed interventions during the retrieval and reconsolidation of memories.
Vision is another important area. NMDA receptors participate in the activity of retinal ganglion cells, and in information processing by the visual cortex. Their abnormal activity has been linked to impaired signaling in glaucoma, diabetic retinopathy, and neurodegenerative diseases of the retina. Prolonged calcium influx may contribute to cellular damage, while chaotic oscillations may introduce structured noise into visual signals that is difficult for the brain to filter out. Understanding the ranges within which neuronal activity remains stable could therefore support the design of retinal stimulation methods and vision restoration strategies.
The authors also point to the potential relevance of their findings to schizophrenia, autism spectrum disorders, Alzheimer’s disease, and chronic pain. Abnormalities involving NMDA receptors or the balance between excitation and inhibition have been reported in all these conditions.
“This is not yet a therapeutic design or evidence obtained from patients. We have produced a map of mechanisms that must now be tested in biological experiments and recordings from real neurons. Its value lies in identifying specific kinetic and frequency ranges instead of treating all NMDA-related dysfunctions as a single problem,” emphasizes Dr Mehdi Borjkhani.
The model represents a single cell and therefore does not reproduce the synchronization of entire neuronal networks or the complex interactions between different regions of the brain. The next step should be to compare its predictions with real electrophysiological recordings and extend the model to the network level. Nevertheless, the study already demonstrates an important principle: the brain encodes information not only through the number of impulses, but also through their rhythm and the length of time for which a neuron’s molecular gates remain open.
Mehdi Borjkhani, Hadi Borjkhani, Morteza A. Sharif, Fariba Bahrami, Mahyar Janahmadi (2026). NMDA receptor kinetics drive distinct routes to chaotic firing in pyramidal neurons. Frontiers in Computational Neuroscience.
DOI: https://doi.org/10.3389/fncom.2026.1753444
Author: Scientific Editor Marcin Powęska
