Title: Teaching Undergraduate Biophysics using Excel
Abstract: A new approach is presented for teaching biophysics to a broad audience, including undergraduates with no calculus background. The classic two-box system from statistical mechanics is chosen as an example, to illustrate how this approach can be implemented. In the sample exercise, students develop a simple Excel spreadsheet "from scratch". This spreadsheet implements a kinetic Monte Carlo (KMC) simulation algorithm. The basic transport mechanism is the transfer of a randomly selected particle from one box to the other. In a directed, activity-based exercise, students write an algorithm for the simulation, check and debug the algorithm using "by hand" calculations. Students then use the spreadsheet they have developed to discover for themselves the consequences of changing the number of particles (N) and the initial distribution of the particles. By analyzing their simulation output, students see how the system approaches equilibrium and how fluctuations in the system depend on system size. By investigating the trend in fluctuations with system size, students discover that fluctuations become negligible in macroscopic systems. Finite difference equations are derived and implemented in an Excel spreadsheet to model the kinetics of the two box system. Students then compare the theoretical predictions for the average behavior of the system with the "random" data from the KMC "computer experiment", to investigate the qualitative and quantitative differences between these microscopic and macroscopic approaches. The students also make a histogram of system states taken from an equilibrium simulation with N=150 particles and compare it with predictions of the binomial distribution for the same system, to demonstrate the preponderance of the most probable states in the ensemble average. This pedagogical approach is quite different from using "canned" computer demonstrations, as students design, implement and debug the simulations themselves - ensuring that they understand the model system intimately.