Single-Channel Monte Carlo Simulation

What is being simulated? This is a generic ligand-gated ion channel rather than a model of one named receptor subtype. Each channel moves randomly among a resting closed state, an agonist-bound closed state, an open state, and a long-lived closed state representing simplified desensitization. A fixed agonist pulse permits binding for the selected excitation duration; only the open state conducts. The transition times are generated by a continuous-time Monte Carlo method.

Reading the left plots. Single Trace Sweeps shows N independent channel records, vertically offset so that openings can be distinguished. Sum Trace is the point-by-point sum of those N currents, not their average. When a channel is open, its current is calculated as i = −γ(E − E_rev); increasing either the single-channel conductance or the magnitude of the driving force therefore increases the current step. Excitation duration controls the agonist pulse, while measurement duration controls the displayed recording window.

Noise and random seed. Noise standard deviation adds independent Gaussian current noise to every sampled channel value. The random seed makes a run reproducible when all other settings are unchanged. Keep it fixed to reduce one source of variation during comparisons, or change it to generate a new realization.

Reading the right plots. Ensemble size is the number of independently simulated repetitions used for fluctuation analysis; every repetition contains the selected N channels. Variance and Mean Current Vs. Time shows the across-ensemble mean and variance at each time point. Variance Vs. Mean plots those same time points against one another. Larger ensembles usually give a smoother and more reliable relationship.

CSV data. Download the current realization’s individual channel traces, summed current, ensemble mean and variance, variance–mean coordinates, parameters, and random seed.

Show Model. This adds the binomial fluctuation relation σ² = iI − I²/N. The overlay uses the selected number of channels and estimates the unitary current from the low-current portion of the simulated variance–mean data. Compare the points with the curve, then explore how a small ensemble or added recording noise makes the estimate less reliable.

Suggested exploration. Begin with the defaults and compare several random seeds. Then change N, ensemble size, conductance, driving force, pulse duration, and noise one at a time. Notice which settings change the size of each opening, the number of available channels, the time course of the summed current, or the scatter around the variance–mean curve.

Model scope. The four-state kinetic scheme is a simplified teaching model and is not a quantitative fit to a particular receptor. Its stochastic Q-matrix approach follows the general framework described by Colquhoun & Hawkes (1995), The Principles of the Stochastic Interpretation of Ion-Channel Mechanisms, chapter 18 in Single-Channel Recording, 2nd edition.