I'm trying to solve an equilibrium problem for the following competing chemical reaction:
AP + P -><- APa@P (K1 = APa@P/(AP*P) = 1e5)
AP + P -><- APp@P (K2 = APp@P/(AP*P) = 1e4)
That is; AP can bind in two ways to P and does so with two different association constants (K1 and K2). I will therefore have 4 species in solution: unbound AP, unbound P, APa@P and APp@P. Knowing the starting concentrations AP0 and P0, fsolve should easily be able to solve all the concentrations by solving the following four non-linear equations:
P0 - P - APa@P - APp@P = 0
AP0 - APa@P - APp@P = 0
APa@P/(P*AP) - K1 = 0
APp@P/(P*AP) - K2 = 0
My function file becomes:
function [Concentrations] = svdConcfunc(D)
global AP0 P0 K1 K2
Concentrations = [P0 - D(2) - D(3) - D(4);
AP0 - D(1) - D(3) - D(4);
D(3)./(D(1).*D(2)) - K1;
D(4)./(D(1).*D(2)) - K2];
My script, calling the above function looks like this:
global conc AP0 P0 K1 K2
options = optimset ('Tolfun', 1e-30, 'TolX', 1e-20, 'MaxFunEvals', 1e20, 'MaxIter', 1e20);
P0 = 2e-6;
K1 = 1e5;
K2 = 1e4;
for i = 1:length(conc);
AP0 = conc(i);
%format = [AP P APa@P APp@P ];
Guessconc = [AP0 P0 AP0 AP0 ];
CalcConc(i,:) = fsolve(@svdConcfunc, Guessconc, options);
test_should_be(i) = P0 + AP0;
test = sum(CalcConc, 2)
test_should_be = test_should_be'
the loaded "conc" becomes:
The output I get is the following:
So the sum of all calculated concentrations in solution is not the same (there is a difference between "test_should_be" and "test") as the sum of what I put in, which is physically impossible and I cannot for the life of me understand why it won't work. I have been able to solve far more complicated equilibrium problems (more equations, species and binding constants) before so this should be a walk in the park.
I have tried to play around with starting guesses and tolerance values but I can't seem to get a better solution.
Any help on this would be much appreciated!
"Jesper" wrote in message <email@example.com>...
> test_should_be(i) = P0 + AP0;
> test = sum(CalcConc, 2)
> So the sum of all calculated concentrations in solution is not the same (there is a difference between "test_should_be" and "test") as the sum of what I put in, which is physically impossible and I cannot for the life of me understand why it won't work. ....
- - - - - - - - -
Though I am not a chemist there seems to be something rather questionable with your test procedure. For every one mole of AP and one mole of P which is converted to APa@P or APp@P you have only one mole of result, but you appear to be requiring in "test=sum(CalcConc,2)" that the total number of moles should remain constant. In other words you may be obtaining perfectly valid solutions but your test looks invalid to me.
A better test would be to check whether your original four equations are satisfied or not for each of the AP0 concentrations.
There is a way you can avoid using 'fsolve' and I don't understand why you are not doing things this way. Your four equations can be reduced to the solution of simple quadratic equations in D1 and D2 (AP and P) in which one of the two roots gives positive values for the concentrations. D3 and D4 (APa@P and APp@P) are then readily found from D1 and D2. Do as follows:
T1 = (-1+sqrt(1+2*(K1+K2)*(P0+AP0)+((K1+K2)*(P0-AP0)).^2))/2/(K1+K2);
T2 = (P0-AP0)/2;
D1 = T1-T2;
D2 = T1+T2;
D3 = K1*D1.*D2;
D4 = K2*D1.*D2;
(These should be valid as vectorized solutions using a vector for AP0.)
I am assuming I have the correct equations to be solved:
D1 + D3 + D4 = AP0
D2 + D3 + D4 = P0
D3/(D1*D2) = K1
D4/(D1*D2) = K2
(You first wrote: "AP0-APa@P-APp@P=0" for that first equation but later added the obviously needed D1 (AP) term.)
You can think of your watch list as threads that you have bookmarked.
You can add tags, authors, threads, and even search results to your watch list. This way you can easily keep track of topics that you're interested in. To view your watch list, click on the "My Newsreader" link.
To add items to your watch list, click the "add to watch list" link at the bottom of any page.
To add search criteria to your watch list, search for the desired term in the search box. Click on the "Add this search to my watch list" link on the search results page.
You can also add a tag to your watch list by searching for the tag with the directive "tag:tag_name" where tag_name is the name of the tag you would like to watch.
To add an author to your watch list, go to the author's profile page and click on the "Add this author to my watch list" link at the top of the page. You can also add an author to your watch list by going to a thread that the author has posted to and clicking on the "Add this author to my watch list" link. You will be notified whenever the author makes a post.
To add a thread to your watch list, go to the thread page and click the "Add this thread to my watch list" link at the top of the page.
A tag is like a keyword or category label associated with each thread. Tags make it easier for you to find threads of interest.
Anyone can tag a thread. Tags are public and visible to everyone.
The newsgroups are a worldwide forum that is open to everyone. Newsgroups are used to discuss a huge range of topics, make announcements, and trade files.
Discussions are threaded, or grouped in a way that allows you to read a posted message and all of its replies in chronological order. This makes it easy to follow the thread of the conversation, and to see what’s already been said before you post your own reply or make a new posting.
Newsgroup content is distributed by servers hosted by various organizations on the Internet. Messages are exchanged and managed using open-standard protocols. No single entity “owns” the newsgroups.
There are thousands of newsgroups, each addressing a single topic or area of interest. The MATLAB Central Newsreader posts and displays messages in the comp.soft-sys.matlab newsgroup.
You can use the integrated newsreader at the MATLAB Central website to read and post messages in this newsgroup. MATLAB Central is hosted by MathWorks.
Messages posted through the MATLAB Central Newsreader are seen by everyone using the newsgroups, regardless of how they access the newsgroups. There are several advantages to using MATLAB Central.
Your MATLAB Central account is tied to your MathWorks Account for easy access.
Use the Email Address of Your Choice
The MATLAB Central Newsreader allows you to define an alternative email address as your posting address, avoiding clutter in your primary mailbox and reducing spam.
Most newsgroup spam is filtered out by the MATLAB Central Newsreader.
Messages can be tagged with a relevant label by any signed-in user. Tags can be used as keywords to find particular files of interest, or as a way to categorize your bookmarked postings. You may choose to allow others to view your tags, and you can view or search others’ tags as well as those of the community at large. Tagging provides a way to see both the big trends and the smaller, more obscure ideas and applications.
Setting up watch lists allows you to be notified of updates made to postings selected by author, thread, or any search variable. Your watch list notifications can be sent by email (daily digest or immediate), displayed in My Newsreader, or sent via RSS feed.
You can also select a location from the following list: