Chapter 3. Instructions for using an Excel spreadsheet for simulation of dopamine overflow in the brain

In this last lesson, we give Excel spreadsheets you can use to begin to develop your own models and model your data.

These instructions are to be used with the Excel files from the download page of our website.

Download the amperometry and the cyclic voltammerty spreadsheets on the downloads page and open it in Excel. If you have a problem with it, email me (ds43@columbia.edu) and I can send it to you as an email attachment.

To the right of the spreadsheet is a chart of the curve resulting from the simulation. There are 3 parameters that can be changed in the cells BR 3, 4 and 5: the maximal uptake rate Vmax, the apparent affinity Km, and the initial dopamine concentration. To see how the Michaelis-Menten parameters alter the curve, try changing the values for the uptake.

How the spread sheet is set up

This version of the simulation uses 51 columns, from column F to BD. If you decide to increase the number of bins, we recommend you use an odd number.The electrode is represented by the middle column (AE) with 25 columns on the left and right. Each column begins at time 0 with the same concentration of transmitter, which you set in cell BR5. The exception is at the electrode itself, and the 'dead space' around the electrode. If you wish to change the dimensions of the dead space, fill in "0" by hand. For most of our data, 6 µm at each side (in this case 3 bins) fit well. This seems reasonable considering a 5 µm carbon electrode enveloped by a layer of glass.

As explained in Chapter 2, the electrode can be modeled as consuming (as in the amperometric spreadsheet), or reflective (as in the cyclic voltammetry spreadsheet): this is the only difference betwee the amperometric and cyclic voltammetry spreadsheets.

The size of the release area is a separate parameter, and becomes more important with low uptake transport activity. This can be adjusted by inserting more columns.

The rows represent a time period that is set by the bin size, using the equation in cell A13. If one wishes to change the diffusion coefficient (set at 2.7 x 10^-6 cm^2/sec), substitute the new value in cell A11. The spreadsheet as prepared contains 128 time rows. Each time point actually consists of two rows, one in plain font, and the other in boldface. As explained in chapter 2, the plain font first uses the random walk formula, and the boldface row then corrects for uptake according to the Michaelis-Menten equation.

The chart

The chart plots time on the X axis from column BI and the concentration on the Y axis from column BG. We used a 4 point smoothing function on column AE, which decreases the noise and makes the function appear smoother. Alternatively, the noise can be decreased by increasing the number of columns and decreasing the bin size.

Questions

1. How wide should the bin sizes be?

We prepared the spreadsheets using bin sizes of 2 µm. However, we generally use bin sizes of 0.5 µm for simulations of data from the brain slice. The spreadsheet sent as an attachment uses a larger dimension, so that the size of the file remains small enough for easy download. We recommend that you try examining smaller bin sizes, and compensate for the total volume of the simulation by pasting new columns. You will see that if the bin sizes are too large, they act as a low-pass filter, and artifactually decrease the maximum peak height. Moreover, the shape may appear jagged rather than smooth. As the bin sizes are moved to smaller values, you arrive at a limit of maximal peak height, providing a more accurate simulation. Again, for our brain slice models, 0.5 micron is a good value, as smaller bins sizes produce a negligible increase in peak height.

2. How wide should the dead volume be?

The dead volume can be adjusted by inserting 0 values in the top time row around the middle electrode column. You will see that this greatly affects the rising phase of the curve. Determine the best fit to your real data with this parameter; smaller dead volumes result in more rapid inclines in the curve.

3. How wide should the release area be?

This parameter is often significant for the fall-off phase of the curve. In slice, we often find our data is well fit by about a 50 µm radius, not far from the distance between our bipolar electrodes. You will need to experiment to find the best fit for your own parameters.

4. How to estimate 'goodness-of-fit'?

We use the R-squared (R^2) statistic for nonlinear regression. A tutorial on this subject is on the GraphPad web site. This widely-used statistic for determining the fit of non-linear functions yields a fraction between 0 and 1 and has no units. Higher values reflect a better fit. The R^2 statistic can be thought of as the fraction of the total variance that is explained by the simulation.

In short, R^2 = 1.0 - (SSreg/SStot), where SSreg is the sum-of squares of the differences between the real data and the simulation trace in units of the Y axis squared (current, concentration, or number of molecules) and SStot is the sum of squares of the differences between the data and a horizontal line through the mean of all the Y values of the data. High values R^2 result if the variance between the simulation and data is substantially lower than the variance between the data and the mean value.

5. Is there a commercial program available for running the Schmitz/Sulzer simulation?

Justin Lee from Synaptosoft has written a computer program that automates this simulation. The algorithm has been incorporated into an analysis program called 'Mini Analysis Program'. In the 'random walk menu' you can choose values for 4 parameters, which are the 'dead radius', initial transmitter concentration, Vmax and Km, and generate a curve in either amperometric or cyclic voltammetry mode. To fit the simulation curve to an actual recording trace, the program runs a simplex algorithm to find the parameters that yield the best fit according to an R^2 criterion. The size of the release area and the diffusion coefficient can be changed. The Mini Analysis Program is available for download at http://www.synaptosoft.com.

Jill Venton, who was in Mark Wightman's lab, has also used commercial software. Download the paper here.