From owner-metabolic-reg@net.bio.net Thu Aug 26 23:00:00 1993 Path: biosci!ciit.org!SCHLOSSER From: SCHLOSSER@ciit.org Newsgroups: bionet.metabolic-reg Subject: A software challenge Message-ID: <9308271433.AA10805@net.bio.net> Date: 27 Aug 93 14:26:00 GMT Sender: daemon@net.bio.net Distribution: bionet Lines: 107 Dear BTK software developers: I'm writing an article on the use of sensitivity anlysis for experimental design (for the toxicology literature) and am trying to identify software on which these calculations are relatively easy. I intend to put a list of the software in an appendix. I've devised a sample problem to test on various programs, given below. (Some of the explanation will be remedial for you, this was written for software companies who don't know what partial derivatives are.) If you have a software package for distribution, I would appreciate it if you would try this problem and provide a demo document or template program for interested users. (I have a Mac &, with some difficulty can access a PC, if I must perform the demo's myself. However this will require becoming familiar with a number of programs and I fear that I might not represent them properly.) The application should be fairly easy, and I'm making decisions on what to include on my list based on ease. (If it can be done, but its a pain in the *** then I won't list the software.) The target audience is people with marginal 'programming' skills. Therefore, I will need to see a copy or description of the programing or model entry/problem definition dialogue that one must perform to get a solution before I can include the software in my list. Also, of course, you'll want to provide info on how to get the software. By the way, Chemical Engineering Progress (trade journal for the AIChE) has an annual software directory. If you're interested in other venues for advertising software, you might contact CEP. Karen Simpson is Managing Editor, phone: 212/705-7337, FAX: 212/752-3294 (once you get the USA). Thanks in advance, Paul schlosser@beta.ciit.org Paul Schlosser CIIT P.O. Box 12137 Research Triangle Park, NC 27709 USA phone: (919) 541-2070, ext. 243 FAX: (919) 541-9015 Simple Example of Sensitivity Analysis for Experiment Design The example system contains two variables/chemical species linked by the reaction x1 -> x2, the rate of which is r = Vmax*x1/(Km + x1). For illustrative purposes, take Vmax = 2/min and Km = 5 mM. We will consider initial conditions with x1(0) = x10 and x2(0) = 0, and incubations up to 90 min in length. The solution is considered to be a function of the parameter values; i.e., x1(t; Vmax, Km) and x2(t; Vmax, Km). In our experiments, concentrations are determined by using 14C labelled compounds, and higher concentrations are obtained by diluting with cold material, so a measurement of x1 = 1.0 mM in an experiment with x10 = 10.0 mM is given the same weight as a measurement of x1 = 0.1 mM in an experiment with x10 = 1.0 mM. In both cases, the measurement would be that of 10% of the initial radioactivity (which is the same in both experiments) being assigned to x1. Therefore, I will define the measurement variables, y1(t; Vmax, Km) = x1/x10 and y2(t; Vmax, Km) = x2/x10 . I want to compute the derivatives, GKm1 = dy1(t; Vmax, Km)/dKm and GKm2 = dy2(t; Vmax, Km)/dKm for various initial conditions (e.g., for values of x10 between 0.1 and 10.0 mM). These derivatives will be a function of time. (Alternately, we could consider the derivatives with respect to Vmax.) I then wish to compute the Information Index e(Km, t) = [(w1*GKm1*GKm1) + (w2*GKm2*GKm2)]*Km*Km, where w1 and w2 are weights (can be taken to w1 = w2 = 1.0 here, but may be different in general). Multiplying by Km2 (i.e., the square of the parameter for which the derivatives were taken) normalizes results, and would be a common feature. The object is then to identify the combination of x10 and t for which e(Km, t) is maximized, and to be able to show a graph or listing of e(Km, t) as a function of time at that value of x10. In short, where is the maximum of e(Km, t) in the region t in [0, 90min] and x10 in [0.1, 10.0mM], and what does e(Km, t) look like for that value of x10? (For notational purposes, e(Km, t) may be denote eKm.) In general, we wish to consider general models in which pools are linked by fluxes, and in which the fluxes can be assigned a user-defined function of arbitrary complexity. The models often contain time-dependent 'control' variables or parameters, such as might occur under periodic chemical exposure (e.g., 6 hrs of continual exposure followed by 18 hrs of non-exposure, or bolus injections every 4 hrs, etc). .