Hello, I'm in need of someone to show me how to fit a bacterial growth curve to data in Prism, preferably using the Gompertz function. I also need someone to show me how to assess the goodness of this fit. I have many different growth curves and I need to compare the parameters. Hopefully, there are some life scientists who are familiar with math and can help me.
I'm not familiar with Prism, but any good statistical package will fit curves to data either by least squares or maximum likelihood estimation (MLE) and estimate goodness of fit. The linked article should help you decide on the choices of models. The Gompertz function is a variation of the logistic model. The inflection point is found by setting the second derivative to 0. The tangent (first derivative) at this point is the slope of the maximum growth rate. The intersection of this line with the t (time) axis gives you the lag phase. These two variables plus the asymptotic limit of growth are the key parameters of bacterial growth models. Are you testing for changes in growth rates caused by antibiotics or other interventions? If so, this paper discusses useful statistical tests for comparing curves. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC184525/pdf/aem00087-0379.pdf
I'm not sure Prism is a good package for this kind of analysis. My choice would be R or SAS. http://www.jstatsoft.org/v33/i07/paper
gompertz Unfortunately, I don't have access to R. I want to fit it to a model instead of using regression because I want some biologically meaningful parameters to compare. Biologically, I'm trying to determine if the CpxR transcription factor is repressing an operon. I've created a cpxR knockout and am comparing it to the wild-type. To compare them, I'm using a Wallac Victor to simultaneously record optical density and luminescence (from my luciferase based transcriptional reporter). I've observed the transcriptional de-repression that I want to see in the luciferase curves. But the growth curves of the wild-type and the cpxr strain are quite different. Somehow I need to be able to compare these to each other. I thought it would be a good idea to fit the OD data to a model so I can get some parameters like lag time, maximum specific growth rate, and maximum value. But there's no basic tutorials on the internet. It's strange because I've taken courses in differential equations and vector calculus but I have no practical experience with this kind of stuff. I don't know what models are appropriate, etc. Essentially, I have no meaningful way to compare to growth curves except to show them side-by-side and say growth is slowed in one. haha it's frustrating
Are you working in an academic setting? R and SAS are widely available in such a settings as well as help for working with the software. If not, I can only suggest you break down the problem to the three basic parameters and do simple t tests for differences in the mean values (for small samples). That is, compare lag time to lag time, etc. These tests can reasonably be done with a hand held calculator and a textbook with t test tables.. Sorry I couldn't be of more help, but to do the kind of analysis you seem to want to do, you need the right tools.
http://cran.r-project.org/bin/windows/base/ you can download, free, the R package here for Windows. If you have linux, most major distributions have an R package as well. Free. I have it on OpenSuse, and cygwin (runs under windows). I seldom use it for what I do. If this is thesis work I'd suggest R. If this is a lab assignment, which I kinda doubt, then you probably are constrained by the package your prof wants you to use.
Hi guys, First of all, thank-you for helping me thus far. I found R for Mac OS X on that cran site and installed it. Turns out they have grofit as well and I was able to install the grofit package. But as a first time user, I'm a little confused on what to do now. I've opened that paper that you posted, SW, and I see some algorithms. How do I input my data and run these algorithms? I have an excel sheet that contains each experiment which is done in 4 replicates with an optical density and time series.
I assume your data is in numerical for for the X and Y axes (time and size reference ). If you're plotting OD directly, you may need to know how that corresponds to bacterial counts in order to get the right shape to your models. Here's some info on inputting data. www.statmethods.net/graphs/scatterplot.html I can't give you complete tutorial on R, but there are a number of them on line. You didn't tell me anything about your work environment, but the description of your work suggests you're a grad student. There should be plenty of resources available to you. If you're familiar with Excel, maybe you should work in that. I don't like Excel myself.