The membrane potential of a cell (such as the resting potential of approximately -70 mV) is the potential difference across the membrane, while “volts per meter (V/m)” is a unit of electric field strength, representing the rate of change of potential over space. To convert the membrane potential into electric field strength, we need to consider the thickness of the cell membrane (i.e., the spatial scale of the potential difference). Below is the detailed derivation process: ###
Key Data and Formulas
1. **Thickness of the cell membrane**: The typical thickness of a biological membrane is about **5-10 nanometers (nm)**. Taking an average value of **7.5 nm (i.e., \(7.5 \times 10^{-9}\) meters)**.
2. **Potential difference (membrane potential)**: Using the resting potential as an example, take **-70 mV (i.e., \(70 \times 10^{-3}\) volts, only the absolute value is calculated)**. 3. **Formula for electric field strength**: \[ E = \frac{\Delta V}{d} \] Where: – \(E\) is the electric field strength (V/m), – \(\Delta V\) is the potential difference (V), – \(d\) is the distance (m). ###
Calculation Process Using the resting potential of **70 mV** and a membrane thickness of **7.5 nm** as examples: \[ E = \frac{70 \times 10^{-3} \, \text{V}}{7.5 \times 10^{-9} \, \text{m}} = \frac{70}{7.5} \times 10^{6} \, \text{V/m} \approx 9.33 \times 10^{6} \, \text{V/m} \] This is approximately **\(9.33 \times 10^6\) volts per meter (9.33 million V/m)**. ###
Analysis and Significance of the Results
1. **Magnitude of the value**: The electric field strength across the cell membrane is extremely high, reaching the order of **\(10^7 \, \text{V/m}\)**, far exceeding the electric fields in everyday environments (e.g., the electric field of a typical battery is about \(10^2 \, \text{V/m}\)). This is because the thickness of the cell membrane is extremely thin, causing the potential difference to form a steep electric field gradient at the nanometer scale.
2. **Biological significance**: – Such a strong electric field directly affects the conformation of ion channels in the membrane (e.g., voltage-gated channels), regulating the transmembrane transport of ions. – The electric field, together with the concentration gradient, constitutes the **electrochemical driving force**, which drives the transport of substances (e.g., the transmembrane movement of Na⁺ and K⁺).
3. **Comparative reference**: – The electric field between a thundercloud and the ground is approximately \(10^4 \, \text{V/m}\), while the electric field strength of the cell membrane is **over 1,000 times greater**, illustrating its remarkable intensity. ###
Notes 1. **Influence of membrane thickness**: If the minimum membrane thickness of **5 nm** is used, the electric field strength is: \[ E = \frac{70 \times 10^{-3}}{5 \times 10^{-9}} = 1.4 \times 10^7 \, \text{V/m (14 million V/m)} \] The range of values can be generalized as **\(7 \times 10^6 – 1.4 \times 10^7 \, \text{V/m}\)**.
2. **Sign of the potential difference**: When calculating the electric field strength, only the absolute value of the potential difference is taken, with the direction pointing from the outside of the membrane (positive) to the inside (negative).
### Conclusion When the membrane potential of a cell is converted into electric field strength, the value can reach the order of tens of millions of volts per meter. This result intuitively demonstrates the strong electrochemical gradient maintained by the cell membrane at the nanometer scale. This characteristic is not only the basis for cellular signal transduction (e.g., action potentials) but also provides a physical explanation for understanding the functions of membrane proteins (e.g., ion pumps and channels).
