# Biological Basis of the VSFP3.1 Model Code The provided code models the behavior of the Voltage-Sensing Fluorescent Protein (VSFP) 3.1, specifically focusing on the voltage sensor domain and its resulting fluorescence response. This biological model captures the dynamics of voltage-sensing in neuron-like cells, providing insights into how these proteins can be used to visualize electrical activity in neural tissues. Below, key biological aspects that are modeled in the code are described: ## Voltage-Sensing Domain - **Voltage Sensor States**: The model includes multiple states corresponding to the conformations of the voltage-sensing domain. These states include closed (S1n, S2n) and open conformations (S1p, S2p). The transitions between these states are governed by voltage-dependent and kinetic parameters. - **Markov Model**: The code employs an 8-state Markov process to describe transitions between different conformational states of the sensor. This captures the probabilistic nature of ion channel gating and sensor conformational changes in response to voltage. ## Fluorescence Reporter - **Reporter States**: The reporter domain is modeled with binary states: 'off' (Rn) and 'on' (Rp), reflecting whether the fluorescent reporter is active. Transitions between these states are modulated by the conformational state of the sensor domain. - **Fluorescence Response**: The fluorescence response of VSFP3.1 is computed based on the populations of the 'on' and 'off' states, allowing the model to simulate how fluorescence signal changes correlate with electrical activity. ## Gating Current - **Displacement Current**: The model calculates the gating current generated by the movement of the voltage sensor's charges across the membrane. This is portrayed through the functions (`gate1Flip`, `gate2Flip`, `gate12pFlip`, `gate12nFlip`) that compute the rate of charge transfer in each transition state of the voltage sensor. ## Biophysical Parameters - **Z-Gating Charges**: These parameters (zGateS1, zGateS2, etc.) capture the effective charge movement during conformational changes, an essential aspect in characterizing sensitivity to voltage changes. These are directly linked to the energy barriers and transitions modeled by the Markov process. - **Thermodynamic and Kinetic Constants**: Transition rates are specified with temperature-dependent scaling factors (`qtGate`, `qtFluo`) based on biological temperature conditions. They incorporate the von Hippel expression for temperature compensation often required in biophysical modeling to simulate room versus physiological temperatures. ## Fluorescence Modulation - **Biological Observability**: The parameter `deltaF` defines the extent of fluorescence modulation, mapping the sensor's electrical state to an optical output that can be measured experimentally. ## Biological Context - **VSFP3.1 Function**: VSFPs are genetically encoded voltage indicators that combine a voltage sensor with a fluorescent protein. They are used to image membrane potential changes in living cells, particularly neurons, offering a non-invasive method to observe neural activity. - **Electrophysiological Relevance**: The model aids in understanding VSFP behavior in cellular environments such as PC12 cells, commonly utilized in neuroscience for studying signal transduction and neurobiology. The code provides a computational framework to simulate the physiological behaviors of VSFP3.1, facilitating exploration of its application in imaging techniques used to observe neuronal circuit dynamics.