The provided code snippet from the file `run_over_Rm.hoc` is related to modeling neuronal membrane properties, specifically the passive membrane resistance value, \( R_m \). Here’s an explanation of the biological basis connected to the code: ### Biological Context 1. **Membrane Resistance (\( R_m \))**: - \( R_m \) is a critical parameter in neuronal modeling that represents the resistance of the neuron’s membrane to ionic current flow. It is inversely related to the membrane's conductance (\( g_{pas} \)), where \( g_{pas} = 1/R_m \). - High \( R_m \) values imply that the membrane is less permeable to ionic currents, leading to slower leakage and thus greater preservation of synaptic input over time and distance. Low \( R_m \) values suggest higher permeability and faster decay of voltage changes. 2. **Passive Properties**: - The code simulates the 'passive' electrical properties of the neuron, meaning it focuses only on the linear, ohmic current flow without considering active ionic conductances provided by voltage-gated ion channels. - These passive properties play a fundamental role in determining how signals (voltage changes) decay over the dendrites and axons of neurons. 3. **Conductance Adjustment via \( g_{pas} \)**: - The parameter `g_pas` in the code refers to the passive conductance of the neuronal membrane. - The assignment `forall {g_pas=1/Rm_vec.x[i]}` iterates over different membrane resistance values, affecting the passive leak conductance and thereby altering the passive response of the neuron. 4. **Relevance in Neuronal Modeling**: - By varying \( R_m \), the model provides insights into how different levels of membrane resistance affect the passive electrical behavior of neurons. - This variation could be used to mimic different types of neurons or conditions under which membrane resistance may change, such as in response to different ion channel expression levels, pathological states, or developmental stages. 5. **Application**: - Understanding the effects of passive membrane properties helps in the study of how neurons process information, maintain resting membrane potential, and influence the speed and spread of electrical signals. This code represents a foundational illustration of how biophysical properties such as membrane resistance influence neuronal behavior, facilitating the exploration of a range of physiological and pathological neuronal conditions.