Chapter 11: Fitting and Statistical Analysis of Single-Channel Records D. Colquhoun and F. J. Sigworth ### 1. Introduction The analysis of single-channel records has two main purposes. The first is to observe the qualitative features of the data, such as variations in current amplitude or grouping into bursts. These features may not be easily visible on an oscilloscope due to heavy filtering. Automated methods are not ideal for this purpose. The second purpose is to perform quantitative analysis of measurable variables, such as channel-open durations, by comparing them with theoretical distributions. This helps infer biological mechanisms. The chapter focuses on analyzing channel current amplitudes and durations, assuming currents consist of rectangular pulses with flat tops and instantaneous transitions. The analysis involves estimating amplitudes and transition times, then fitting distributions to these estimates. Analyzing single-channel records is time-consuming due to the randomness of recorded events, such as channel-open durations. For a quantity with an exponential distribution, the standard deviation of the mean is τ/√n. To achieve 10% accuracy, at least 100 observations are needed. However, more are often required because the distribution may not be exponential but a sum of exponentials. For complex distributions, 1000–2000 openings may be needed for reasonable precision. ### 2. Acquiring Data #### 2.1. Transient Recorders Transient recorders can analyze moderate numbers of events without a computer. They can be triggered by events and display the whole event on an oscilloscope. This method is convenient for producing pictures but too slow for large-scale analysis. #### 2.2. Computer On Line or from Magnetic Tape Data is usually recorded on an FM tape recorder for later analysis. In experiments where ion channels open in response to membrane potential changes, the experiment can be connected to a computer. The computer can supply voltage pulses and acquire data, allowing real-time data manipulation and inspection.Chapter 11: Fitting and Statistical Analysis of Single-Channel Records D. Colquhoun and F. J. Sigworth ### 1. Introduction The analysis of single-channel records has two main purposes. The first is to observe the qualitative features of the data, such as variations in current amplitude or grouping into bursts. These features may not be easily visible on an oscilloscope due to heavy filtering. Automated methods are not ideal for this purpose. The second purpose is to perform quantitative analysis of measurable variables, such as channel-open durations, by comparing them with theoretical distributions. This helps infer biological mechanisms. The chapter focuses on analyzing channel current amplitudes and durations, assuming currents consist of rectangular pulses with flat tops and instantaneous transitions. The analysis involves estimating amplitudes and transition times, then fitting distributions to these estimates. Analyzing single-channel records is time-consuming due to the randomness of recorded events, such as channel-open durations. For a quantity with an exponential distribution, the standard deviation of the mean is τ/√n. To achieve 10% accuracy, at least 100 observations are needed. However, more are often required because the distribution may not be exponential but a sum of exponentials. For complex distributions, 1000–2000 openings may be needed for reasonable precision. ### 2. Acquiring Data #### 2.1. Transient Recorders Transient recorders can analyze moderate numbers of events without a computer. They can be triggered by events and display the whole event on an oscilloscope. This method is convenient for producing pictures but too slow for large-scale analysis. #### 2.2. Computer On Line or from Magnetic Tape Data is usually recorded on an FM tape recorder for later analysis. In experiments where ion channels open in response to membrane potential changes, the experiment can be connected to a computer. The computer can supply voltage pulses and acquire data, allowing real-time data manipulation and inspection.