The provided code models the electrical properties of a neuronal membrane using a simplified equivalent circuit model that includes a membrane capacitance, a leak conductance, and associated parameters. Here's a breakdown of the biological basis of the model: ### Membrane Capacitance (Cm) - **Biological Basis:** The membrane capacitance represents the ability of the cell membrane to store and separate charge. It is a fundamental property of the lipid bilayer and affects the membrane's ability to change potential in response to ionic currents. - **Model Representation:** In the code, `Cm` is specified as a parameter in nanofarads (nF). It influences the capacitive current, which is derived from the rate of change of voltage across the membrane over time. ### Leak Conductance (gL) - **Biological Basis:** Leak conductance represents non-specific ion channels that allow passive ion flow across the membrane, contributing to the resting membrane potential. These channels are often permeable to multiple ions, contributing to a consistent baseline current. - **Model Representation:** `gL` is a parameter in microsiemens (uS) and models the constant leak pathways present in the membrane. It affects the leak current that stabilizes the membrane potential towards the leak reversal potential. ### Leak Reversal Potential (EL) - **Biological Basis:** The reversal potential (also known as equilibrium potential) for the leak conductance is biologically determined by the relative permeability of the ions involved. It is the voltage at which there is no net flow of ions through the leak channels. - **Model Representation:** `EL` is specified in millivolts (mV) and determines the driving force for the leak current. ### Delay - **Biological Basis:** In a biological context, delays might represent axonal conduction delays or synaptic integration timing. However, in this model, the delay primarily allows simulation of transient effects like input time shifts. - **Model Representation:** The `delay` parameter is specified in milliseconds (ms) and is used to shift the voltage trace temporally, allowing dynamic adjustments during fitting. ### Offset - **Biological Basis:** The offset can account for baseline noise or standing currents that may not be captured by just the sum of capacitive and leak currents. - **Model Representation:** The `offset` is specified in nanoamperes (nA) and adds a constant current to the output of the model function. ### Integrated Function (`cap_leak_int`) - **Biological Basis:** The integrated function represents the combined current from the membrane capacitance and leak channels over time, which defines the passive electrical properties of a neuron. - **Model Representation:** The function calculates the total membrane current combining capacitive current, leak current, and any additional voltage-dependent currents, modeling the temporal evolution of the membrane potential in response to changes in voltage over discrete time steps. ### Voltage-Dependent Current (`v_dep_I_f`) - **Biological Basis:** Voltage-dependent currents account for the activity of ion channels that open or close in response to changes in membrane potential, such as potassium, sodium, or calcium channels. - **Model Representation:** The property `v_dep_I_f` allows an additional current to be included, which can be a complex function of voltage, used to simulate specific, variable ion channel behavior not covered by simple capacitance and leak components. In summary, the code models the basic passive properties of the neuron represented as an RC circuit, contributing to understanding the baseline behavior of neuronal excitability and the integration of synaptic inputs.