The provided code is focused on modeling aspects of neuronal behavior using a computational framework that builds cumulative distribution functions (CDFs) from probability density functions (PDFs). Specifically, it appears to be simulating aspects of inhibitory synaptic transmission in the brain, involving network interactions mediated by GABA (Gamma-Aminobutyric Acid), a primary inhibitory neurotransmitter. ### Biological Basis 1. **GABAergic Inhibition**: The code is constructing CDFs for neuronal response types typically classified into two main categories: - **RS (Regular Spiking) Neurons**: These are generally excitatory and are associated with neuronal populations like pyramidal cells. - **FS (Fast Spiking) Neurons**: These are usually inhibitory and are associated with interneurons, particularly those releasing GABA as the neurotransmitter. The `pp_cumulative_FS` variable is clearly named to suggest an association with fast-spiking, likely GABAergic, neurons. 2. **Cumulative Distribution Functions**: CDFs in this context are used to model the probabilistic behavior of GABA receptor activation in postsynaptic neurons. Activation of GABA receptors typically results in hyperpolarization of the neuron, making it less likely to fire an action potential. The inverse of the CDFs suggests an interest in understanding the input distribution necessary to achieve specific responses within these inhibitory synapses. 3. **Probability Density Functions**: The inclusion of functions like `GABA_density` implies a focus on how the continuous distribution of GABA release or receptor activation might influence neuronal behavior. This likely models temporal and spatial dynamics of GABA in synaptic transmission. 4. **GABA Receptor Types**: Though not explicitly mentioned in the code, the modeling may implicitly relate to the dynamics of GABA_A or GABA_B receptors, which mediate fast (ionotropic) and slow (metabotropic) synaptic inhibition, respectively. Gaussian variants used in the code suggest the underlying synaptic processes could follow normally distributed patterns, perhaps due to random synaptic release events or variability. 5. **Integrative Function of FS Neurons**: FS neurons play a crucial role in shaping network oscillations and synchronizing neuronal populations. By generating inhibitory control over excitatory neurons and modulating their activity with high precision, FS interneurons support cognitive processes like learning and memory. 6. **Importance of Delta**: The parameter `delta_2` may represent variability or perturbations in the system, such as changes in neurotransmitter concentration or synaptic efficacy, which can affect the inhibitory outputs of FS neurons and, subsequently, the control of network excitability and plasticity. ### Conclusion This code provides a mathematical framework for understanding the behavior of GABAergic transmission in neural circuits. By modeling the probabilistic distributions underlying synaptic inhibition, it seeks to elucidate the role of inhibitory interneurons in modulating neuronal network dynamics. Such models are critical for exploring how dysregulation in GABA signaling could contribute to neurological and psychiatric disorders.